Can I apply for the STV eVisa while still in Thailand before leaving for Christmas?

I don't know the answer to your insurance question, but (and this still isn't an answer) as far applying for your new e-visa before you leave, the answer is we don't know. The system is too new and no one has tried (or at least not reported back here if they did) yet. In theory it should be possible, but you are also required to send all of the stamps in your passport from the last 12 months as part of your application, so theoretically they could question it or deny it if they aren't happy about it. The only way to know at this point is to try, and if you do decide to try, please report back to us so we know for others.