Why not get a COE for Phuket, one week stay then fly to Bangkok. Get visa on arrival. Unless they change it to Bangkok sandbox and do the same in Bangkok. Take care of immigration a few weeks after arrival?
Update-thank you all for the advice-went to immigration with the US Embassy Letter. They gave me an extension until October 11. Told me to call them on the 11 th for further extensions. Not sure why the call but at least I don’t have to leave on the 26th. Again, thanks for the good advice.