What are the requirements for extending a Non O-A visa in Thailand without health insurance?

It looks like your options are:

1) Go to your local immigration office and try to have them "correct" the stamp (others have had success with that approach).

2) Buy the Thai insurance and be done with issues for a year.

3) Leave then try to enter again without insurance (maybe at a different entry point) and hope that you succeed, even with the 30-day stamp, which may have an annotation in Thai about a lack of insurance.

4) Same as (3) but buy travel insurance to show. Now your risk may be lower than in (3) but your costs would be higher and with no guarantee it would work.

5) It may be possible to change passports and abandon your current O-A visa and get a different visa but I'm not sure about that. Others may know.

6) Find a foreign insurance company that is willing to fill out the foreign insurance certificate on the site Robert Lagas linked to and buy insurance from them. Immigration officers should accept that certificate as proof - *this is speculation on my part* - but since that form is good for people who are applying for O-A visas now, it should work for you too.

I'm not sure if there are any other options for you until your visa expires.

I would try (1) first. If they refuse then look at other options.

If you decide to go for (2) and don't really want health insurance for some reason, I understand that Pacific Cross have plans which can offer steep discounts for high deductibles.