If your country of residence is in the UK you must apply from there. And the amount will have to have been in your UK bank account for the past 6 months. Once the visa has been approved you can spend it as you wish.
Are you certain you cannot get a certificate of residence from the US consulate or embassy? I've gotten them numerous times from the consulate in Chiang Mai on visa exempt.
I hope you're right about that. I know of two friends here in the US who were denied visas (METV) and both lost their $200 application fee. Thankfully I haven't after three applications.
I just completed a 5 month visit to Thailand. I showed evidence of my both my arrival flight and my final departure flight. I took care of the two required exits while there.