Hi Blue,
Well I am in the same pickle as you, at age 76. My advice is to not focus on a "reliable" insurance company, but rather a "cheap" one who will cover us? Why do I say that? Well the chance that you are going to be able to collect on this insurance is just about zero -- there isn't one of these companies which will cover "pre-existing conditions" and those of us (at this tender age) are likely to have something which sounds like a "pre-existing condition" and gives them a ready-made excuse for denying your claim.
So get any old "fly by night" company policy, as long as it gets you in the door, and self-insure yourself against any major healthcare expense. Sadly, this is the reality. And yes I am also hoping this nonsense requirement will be lifted later in the year.
(To find lists of the fly-by-nighters, do the following google search: thailand tourist health insurance for seniors over 75.)
Good luck!