https://www.cbsa-asfc.gc.ca/do-rb/offices-bureaux/658-eng.html

This is the customs and immigration office, if you cross inside the park. (There is a highway border crossing along the east margin of the park, at Chief Mountain, that would be a perfectly suitable place to cross for certain.)

If you are going to be hiking when you cross into Canada, it looks like you can submit to inspection here. You should call the boat operator (you'll be arriving by boat, it appears) to see if this is a problem, and to inquire about how to secure tickets. (I think they normally provide a round trip from Canada.)

If you want to talk to Canada Border Services Agency to check first (and I recommend you do), you can contact them via numbers listed here https://www.cbsa-asfc.gc.ca/contact/bis-sif-eng.html . At the time of posting, there is a toll-free number that will only work in Canada and the US, and two numbers you can dial from overseas - the area code 204 number is in Winnipeg, much closer than the other (New Brunswick) and would probably be the more suitable one.

To clarify, the Canadian customs office is not really an office; you report by telephone. If CBSA wants to inspect you, they will have you wait on the boat for their arrival. You will not be allowed to disembark until approved or inspected.

Jim MacKenzie's advice to contact the CBSA directly is probably the best course of action. If you do so, please come back and post their advice as an answer to your own question so that other people can see it in the future.

That said, if it turns out to be impossible to cross the border at Waterton Lake, you have another option. The Continental Divide Trail (on the US side) branches into two forks near Lake Sherburne (as can be seen on the map here.) One fork goes to Waterton Lake; the other goes to the highway border crossing at Chief Mountain. Moreover, Tamarack Mountain Outfitters offers a daily shuttle service between the Chief Mountain border crossing and the Waterton, AB townsite. The Chief Mountain border crossing is a "normal" border crossing, and is open during daylight hours during the summer.

Of course, the spirit of thru-hiking is generally that you don't want to get off the trail if you can avoid it; however, there are other options available should they be necessary.

First from your quoted info

It is a Class B Port of Call, which just means it is for US and Canadian citizens and permanent residents only.

This doesn't appear to be true. From the CBP site:

Class B means that the port is a designated port of entry for travelers who at the time of applying for admission are lawfully in possession of valid Permanent Resident Cards or valid non-resident aliens' border-crossing identification cards or are admissible without requiring a waiver of inadmissibility.

So it is not just for US and Canadian citizens.

The National Park Service pages on Glacier have several pages on international crossings, but they deal more with travel south into the US. Even so, they reference crossings here by foot and confirm that normal procedures should be to call the Canadian folks after crossing.

https://www.nps.gov/glac/blogs/international-hiking.htm

Welcome to the first International Peace Park in the world! Glacier National Park in the United States and Waterton Lakes National Park in Canada combined in 1932 to become the Waterton-Glacier International Peace Park. This designation allows backpackers to hike continuously from one country into the other through an area known as "Goat Haunt."

When entering Canada from the U.S. you must call Canadian Customs at (403) 653-3535 for acceptance/rejection by Canadian authorities as soon as you arrive in Waterton Townsite. Read all the details under "Entry and Exit Information for Goat Haunt" on our trail status page!

Trail Status Page (https://www.nps.gov/glac/planyourvisit/trailstatusreports.htm)

Entering Canada at Waterton Townsite

Waterton Townsite is NOT a Canadian Port of Entry therefore all arrivals to Waterton Townsite must phone Canadian Customs without delay at (403) 653-3535 or (403) 653-3009 for acceptance/rejection by Canadian authorities. More Information on contacting Canadian Customs is available at the Waterton Lakes Visitor Centre or the Waterton Station of the Royal Canadian Mounted.

The three other answers here were posted in Dec. 2017. But U.S. Customs pilot project expands to Waterton Lakes National Park - Lethbridge | Globalnews.ca started in June 16 2018.

U.S. Customs pilot project expands to Waterton Lakes National Park

By Tom Roulston Global News

Posted June 13, 2018 7:11 pm

U.S. Customs and Border Protection (CBP) is rolling out a new pilot program in Waterton Lakes National Park for pedestrians who will be crossing the Canada-U.S. border into Glacier National Park.

The Reporting Offsite Arrival-Mobile (ROAM) application, available for Apple and Android devices, will allow park visitors crossing into the U.S. via boat or on foot the ability to report their arrival to Customs officials remotely.

The program will launch on June 16 with four inspection kiosks stationed at the Waterton Cruise Company dock.

There, travellers can create a profile and declare their intended trip to the United States.

The ROAM app will also give boat passengers and hikers the option of reporting their arrival from any location via their smartphone.  The app enables a video conference with CBP officers.

It's better quote news article from CBP themself. I emphasize "backcountry" for you.

CBP expands ROAM app pilot to Glacier National Park | U.S. Customs and Border Protection

SWEETGRASS, Mont. — U.S. Customs and Border Protection Office of Field Operations is pleased announce the addition of Waterton, Alberta, to the list of pilot locations now using the new Reporting Offsite Arrival-Mobile (ROAM) application for pedestrian reporting.

CBP has expanded it's ROAM app pilot
program. This pilot expansion includes
pedestrians traveling to Goat Haunt,
Montana, via the International Cruise
Line and/or backcountry hiking trails
via Waterton International Peace Park
in Alberta, Canada, and Glacier National
Park in Montana.

This pilot expansion includes pedestrians traveling to Goat Haunt, Montana, via the International Cruise Line and/or backcountry hiking trails via Waterton International Peace Park in Alberta, Canada, and Glacier National Park in Montana.

This pilot addresses a pressing issue for border waters and backcountry trails that depend heavily on tourism. Vacationers and outdoorsmen from around the world travel to these border areas with their families to enjoy both countries’ national parks. Oftentimes these groups travel into the United States by way of the Waterton Shoreline Cruises in Waterton which requires checks by U.S. Customs and Border Protection at the Goat Haunt Port of Entry when the intent of the traveler was to cross into the United States and hike backcountry trails in Glacier National Park. 

The new pilot program will launch on June 16 at Waterton Cruise Company, which docks in Waterton. It is designed to allow travelers intending to cross into the United States via the international cruise line to be inspected by U.S. Customs and Border Protection through the ROAM application. Four inspection kiosks will be stationed at the Waterton Cruise Company docks for travelers to create a profile and declare their intended trip into the United States.

The ROAM app allows boat passengers and hikers the flexibility of reporting their arrival into the U.S. from any location via a device that is capable of 4G/LTE or Wi-Fi. The ROAM app is available in the Apple and Android stores under CBP ROAM. The ROAM app enables a video conference with CBP officers to efficiently make entry into the U.S.

Intending visitors to the United States can construct a profile within the application, and submit their information for a CBP video conference while at the docks, waiting to board the International vessel. Traveler information can be easily saved within the app, or recreated for future crossings.

CBP's remote arrivals app to launch nationwide -- FCW

• By Mark Rockwell
• Jun 15, 2018

Near Waterton Lakes National Park in Canada (above), a U.S. border crossing app recently went live. (Photo credit: Jason Patrick Ross/Shutterstock)

A new mobile app from Customs and Border Protection will make life easier for pleasure boaters and hikers in border areas, while freeing up border agents for enforcement operations.

CBP hopes its Reporting Offsite Arrival-Mobile (ROAM) app will be useful for small boat operators and their passengers, as well as hikers and other outdoors enthusiasts, who enter U.S. waters and territories in their travels in border regions.

The app is for travelers who want to be processed by CBP upon entry into the U.S.

"Most travelers want to be compliant" with immigration law, and the app makes it easier to do that, said Christopher Wright, program manager for CBP's office of field operations--innovation.

Use of the app by travelers will free up agents to enforce immigration rules against travelers who don't want to comply, according to Wright. The app "is more a reallocation" of agents from compliance work to enforcement, he said.

The app works on LTE- or Wi-Fi-capable mobile devices and allows CBP agents to initiate a video chat after travelers set up a login and profile. Wright said CBP has also partnered with Wi-Fi-equipped local businesses in remote areas where cell coverage is limited and set up kiosks at those businesses.

ROAM replaces CPB's Outlying Area Reporting Stations (OARS), which uses 90's era, one-way video transmission capabilities and speakerphones at remote marinas and docks. Those systems, according to the agency, are outdated and challenging to access.