My girlfriend lives in the UK and I want to be able to come and leave as I please for next 3 years—which visa should I get?

Standard visitor visa seems like it's not long enough.

I would like to come and go as I please. I would like to add I'm currently in the UK, have been here for 3.5 months.

There's no way to do what you want. As a US citizen, there is no visa you can apply for which gives you anything above your visa-free entitlement to apply for entry for 6 months at the border, as you have been doing so far. Unless you apply for a settlement visa.

I will be traveling to Germany soon for work, then coming back, then leaving the UK for a few months, but would like the option to come back after that if I want to (September 2020).

As a US citizen, you can use the ePassport gates, as I'm sure you know. These gates use an unknown function to determine whether an individual should be rejected and sent to speak to a border officer. It's likely that long stays in the UK are a factor in determining whether you'll be required to speak to an officer and justify the purpose of your visit, and your ability to support yourself.

I work remotely, will continue to do so, and am able to show any authorities that I don't plan on moving here permanently.

You are currently breaking immigration law. You are not allowed to work while visiting the UK. It doesn't matter that this work is being done remotely. Doing a little remote work while on holiday is a bit of a grey area, but if you are staying for long periods in the UK, while depending on remote work to support yourself, you are certainly breaking the law, and if found out you will be denied entry to the UK, and will possibly incur a ban as well.

I want to avoid being denied entry in September as I will have stayed here from March 10-July 17 2020, which is encroaching on the 6 month limit.

If you're planning to live long term in the UK, you should apply for a settlement visa. Since you work remotely for a foreign company, this could not be a Tier 2 work visa, unless your company has a UK division which is willing to sponsor you. You could consider the Global Talent visa if you are highly skilled and work in a qualifying field. The remaining option is a family visa on the basis of your relationship with your girlfriend. Since time spent with her while visiting the UK does not count as cohabitation for the purposes of the unmarried partner visa, you'll need to marry or enter a civil partnership with her to qualify.

The UK (and many other countries) have a rather odd (to you) view on remote work. You're not allowed to do it there on a visitor visa. So stop!

Interview with UK firms and get a job with one, that lets you work where you would like to be located, and that is of a type that qualifies you for a long term UK visa. Given that you stated that you want a visa that will let you re-enter the UK at will for years, that is the most easily obtained visa that will do that.

However, once you have that you may want to think about accruing UK residency so you can make a bid for citizenship. Presumably your partner does not want to come to your home country permanently...

To do what you're intending, I think your only available option is to get pre-settled status in the UK via the Surinder Singh route. Essentially it involves:

1. Move to Germany with your girlfriend
2. Stay until end of year
3. Apply for EEA Family Permit, so that you get it before end of 2020
4. Come to UK with EEA Family Permit
5. Apply for Settled Status

Potential pitfalls:

• Relationship not deemed as long-subsisting (can't remember the right term but it's something like this) - usually this means you have to have been together 2+ years. Alternatively you'd need to get married first.
• The short-term nature of your stay in Germany could be perceived as trying to circumnavigate the rules, so you'd need good reasons for moving there and back again.

More information: https://www.ein.org.uk/blog/family-members-british-citizens-surinder-singh-route-after-brexit