Can I board a closed-loop cruise to Alaska with a Canadian port call, with just a US Green card?

Holland America's travel documents say:

For Non-U.S./Non-Canadian Citizens:

You must have and carry a passport valid for six months beyond the duration of your travel. Please carefully verify the existing identification requirements for your particular travel situation. In addition, non-U.S. citizens who have previously been admitted to the United States for permanent residence must carry their Permanent Resident Card (Form I-551), commonly known as a Green Card. Resident aliens not in possession of this must obtain one at the nearest office of the U.S. Immigration Service.

[...]

Guests are responsible for verifying and obtaining any necessary travel documents for entry and exit to the countries visited, as these requirements vary depending on the specific port and nationality of the traveler. This includes payment of all costs related to arrangements to obtain entry to the countries you visit. Boarding may be denied or fines levied against those guests arriving at the pier without the proper documentation, and those guests will not be eligible for a refund. Payment of any fines levied is the responsibility of the individual guest. Please note that fees and visa requirements are subject to change without notice.

In short, you must have a passport valid for six months beyond the duration of your travel and a green card with you if you're not a US or Canadian citizen. No exception is listed for permanent residents to travel without a passport. That's the cruise line's rule regardless of any government regulations that would allow you to travel with less. The cruise line is the final authority that determines whether you can board, and it can make its own rules about travel documents.

You can always contact the cruise line, but if they tell you that you can travel, I'd want that in writing, and you're still entirely at the mercy of the staff at the port, who could refuse you boarding anyway.

According to the Seattle Times:

For “closed-loop” sailings such as Seattle-Alaska cruises that depart and return to the same U.S. port, U.S. officials say that a passport or one of the new alternative documents isn’t required — that a birth certificate and government-issued photo ID, such as a driver’s license, are sufficient (those documents are needed to prove both a traveler’s identity and citizenship). However, some cruise lines strongly urge cruise passengers to have passports. So check — and double-check — with your cruise line. (And you must have ID even if you’re not planning to get off the ship in Victoria.)

So I'm interpreting it as you do not need a passport since your cruise is "closed-loop". If it were me, I would bring the expired passport just in case. If you don't get off the ship in Canada, then you shouldn't have a problem.

But you should check with Holland America just to be safe.