FYI - you asked about your "60 day visa", but what you seem to have meant was your "visa exemption". Please note that this is NOT a 60 day visa. It is a VISA-FREE entry, eligible for residents from 93 countries.
you can use the search funtion in this group to read about other peoples experiences at the embassies/consulates in neighboring countries. Unfortunatly information as to how long it took from application to approval won't be of much use to you, since most of the neighboring countries switch to e-visa October 8. The processing time for applications in those embassies/consulates will be posted on their websites, but I'm sure it might change/vary over time since the process is new to them.
As others suggested you should consider Taipei or Jakarta if you want to apply in person and have it done in a few days.
I've read about cases where 1 medical appointment have been enough, but I think most embassies/consulates ask for a treatment plan/follow up appointments.
Workcation (remote work, freelancing etc) is one way to go... The other is "Softpower" such as Muay Thai training, Thai cooking classes, Medical treatment, events related to culture etc.