@Jason ******
IF you can prove you meet the insurance requirements (which at this time are
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out/in-patient coverage BUT will go to 100K USD general health coverage in Sept/Oct <-9no one is sure WHEN exactly) you could certainly get stamped in for the 3 months
I'd just leave the country AFTER your current VISA sticker expires (Sept 14th) go to a thai consulate nearby and get a single entry tourist visa, come in get 60 days and extend that by 30 more at the immigration office.
That to me is the easier of the choices