Currently the US is eligible for the phuket sandbox. The only countries that are high risk are those with the Indian variant which are already blocked from flying into Thailand.
Over 150 million Americans have already been vaccinated.
So 2 things, the vaccines in the US (in NJ anyway only Pfizer and Moderna are avaliable) require a minimum if 21 days between 1st and 2nd shot. You wouldn't be able to get vaccinated on a 10 day trip.
2nd, the COE is issued by email almost always in a few hours (within 24 hours by their policy) unless there's an issue with your documents.
Lol, I know you meant quarantine but I still laughed.
Current proposal for the phuket sandbox starting July 1st is that vaccinated people don't need to quarantine but must stay in Phuket for 14 days. The Thai embassy in the US currently doesn't have any guidance on it because it's not official yet contrary to some people's beliefs.
At this time the only way to get into Thailand is by quarantining. If you wait a couple weeks that very well could change.
Yeah embassy is useless for most things unfortunately. Thailand and technology don't go hand in hand, everything online is always a problem.
Just keep trying, try a different browser (chrome, safari, internet explorer). Someone just had this issue 2 days ago, if you scroll through you should see it, maybe they found a different solution.