Since I wont be able to get in for over a month, then it takes 3 weeks to get a new passport and then I need to get in for an in person appointment for FLR(M), I'm worried that it will come close to me overstaying my visa.
If necessary, can you apply by post for FLR(M)? That way you would only need to get the application in the mail before your visa expires.
The processing times are pretty steady at about 6-7 weeks, so unless you need your passport urgently, it may be worth saving the £590 for an in-person appointment.
I have read previously that I can get my FLR(M) under my maiden name, then apply for a name change for my US passport and begin using my new last name then with the only caveat being that I would need to bring both passports to travel. This way I could still change my name without having to wait an extra few months for my FLR (until which, I cant work) and I would get to use my new name without having to pay to move my visa. Does anyone know the specifics on this route?
No, you can't do it this way (2 passports).
If you change your name in your passport you MUST change your name on your BRP card within 3 months or you can be fined £1,000 and have your visa shortened. And it's a big hassle to change it after the FLR(M) has been granted.
It costs £336 to change your name on the BRP and takes up to 6 months to be processed, during which you would be without your passport and visa, so I would not recommend doing this.
Your options:
1) Try to get the name change done before you apply for FLR(M)
OR
2) Apply for FLR(M) in your maiden name and keep your passport in your maiden name. You could then change your name on it within 3 months before applying for the second FLR(M) so you don't have to change the BRP name too.
If I decide to not legally change my name until my 2.5 year FLR(M), in what instances can I use my married name? Obviously nobody would know the difference on social media and such, but as far as CV, bank information, bills, US license, credit cards, GP registration, do I need to continue to use my maiden name?
In the UK, you can just start using your married name for everything except your passport. You just contact the companies (bank, utilities etc.) and ask them to change your name on the account. If necessary, you just show your passport along with your marriage certificate.
Not sure about US stuff, but since you live in the UK, it's not so important to change your US details.
And last question, does anyone know what the timeline is looking like currently for FLR(M) in person appointment availability (or know how I can check?) or how long FLR(M) are taking by mail?
By mail it's about 6-7 weeks.
For in-person appointments you can book up to 42 days (6 weeks) in advance and there are usually plenty of appointments available.