If you have a serious health issue, you have the option to move back to the US and get health insurance via the Healthcare.gov exchange. Anytime of the year, you're eligible to start health insurance that also covers pre-existing and depending on income may get credits to reduce the premiums.
Only risk is an emergency or accidents. Self pay in Asia or an Asia centric plan that could include limited coverage for short trips to US.
*US plans via the exchange start the 1st of the month IF you sign up by the 15th of the previous month so there's a minimum wait of 2 weeks, maximum wait of 6 weeks (if you signed up on the 16th).
Because you must transfer 800k baht to sit in a Thai bank (exchange costs). Interest is almost nothing (or nothing) and if/when you eventually want to transfer it back, there's the hassle (Thailand has stricter transfer out rules), and exchange cost plus rate may/may not be worse.
Keeping that $ in a CD pretty much pays for agent to handle it all for you with no exchange hassles/risks.
If it's a girlfriend, your chances are close to zero unless your gf has strong ties showing she'll return to Thailand (underage children still in Thailand, long term business ownership, etc..).
Also, unless she's very old (40s/50s) then there's the assumption of sex trade.
Best chances are older with ties and applying for tourist reasons with proof of reservations for stay and scheduled tourist activities NOT mentioning coming as a girlfriend.
I renewed in person at the US Embassy in Bangkok. Very easy. I didn't want any issues with the mail so I also requested it to be held for pickup when ready and to be notified. It took about 3 weeks. I went back to Bangkok for a 2nd visit to pick it up. Zero risk that way.
If you don't want your US banks to tell you that you need to close your bank accounts (your US credit cards would be next) you need to keep a physical US home address on your bank profiles. Family/friend address would take satisfy this. Setting everything to electronic minimizes postal mail and you could sign up for a mail service for any limited physical mail. These services are cheap ($120/yr) and offer opening and scanning mail pieces for small extra fees. These services CANNOT be used for home addresses.
The blame would be with your airline (*ie. your responsibility) therefore, Immigration is not going to ignore an overstay. You'd need to apply for an extension or contact your airline to change to a different flight on an earlier date within your 60 days. Your airline should not charge you for that change.