The Evisa website lists United Kingdom and British Overseas Territories so you should have applied to London in the first place. London is usually very quick with visas so you might be ok.
You can extend the Visa Exempt entry by another 30 days at an immigration office without a problem. You might have an issue at check-in with the airline insisting on a flight out of Thailand within 30 days. Some check and some don’t.
If they make a fuss you can say you intend to visit Singapore or somewhere else nearby and be prepared, if necessary, to book the flight there and then.
you need to be resident there, which you say you are, so you will be honest. They will want to see a flight from there to Thailand and, depending which visa you want, bank statements, maybe proof of address etc etc. I know someone who was in a similar position and applied while still in Thailand as was only going to be back in Chicago for a few weeks.
There’s nothing stopping you applying for the visa online before you get back to the US. You’ll need proof of your address etc from there and the flight details from there to Thailand. It’s all done online so you don’t even need to be there when it’s approved. I understand some Consulates there are quite slow and less than helpful so 2 weeks probably won’t be enough if you wait until you’re home before applying.