you can definitely make an appointment to get a certified copy of your passport from the embassy. They do that on a regular basis. When you apply for the appointment you apply under requesting a notary..
I had to get a certified copy of my passport from the US Embassy as well couldn’t get a reasonable timeframe appointment in Bangkok so made appointment with the US consulate in Chiang Mai. It turned out to be a very nice trip. My wife and I took the train up And I got the appointment within 10 days of me applying. A couple of years ago I actually went to three branches of Bangkok bank in Bangkok, and they all were requesting a certified copy of my passport.
yes he is. He’s restarting the countdown to 180 days on the new stamp. you know his phraseology doesn’t have to be perfect for someone to know what his intentions were to say. Are you an English teacher?
As it stands right now, if what you’re saying is correct and you don’t have a visa you will be entering on a visa exempt for 60 days coming from the United States 
yeah sorry I didn’t read the first part of your post saying how many entries you already had. Just to the point though most people do go through fast track thinking that they are getting ahead of everyone in line waiting to go through immigration and all they are doing is getting to the baggage carousel before anyone else.
if you are a legitimate tourist with a UK passport, and have no previous immigration issues ,you are visa exempt for 60 days. There is no reason for them not to allow you entry into the kingdom. It makes no sense to pay an agency and would be a waste of money to pay an agency for a fast track through immigration because you will still have to wait for your luggage just like everybody that is not in fast track. Getting your luggage from the Bangkok airport is the most time consuming part of getting out of the airport. So if you do pay for a fast track service, all that means is you’ll be waiting longer at the baggage carousel for your luggage, unless of course you did not check a bag and had only carry-on.