Believe will be difficult to find a one month policy now that you are in Thailand unless you are on a longer term visa. At least this has been my experience. It is no longer travel type medical insurance. Your current provider may be able to provide a one time extension. My understanding is the doctor that contacts you if tested positive has a lot of say in where you end up doing quarantine. Am sure those with more solid knowledge will comment. I think some people have been able to quarantine at their hotel but depends on situation and not sure of cost. Most insurance just covers medical related expenses for Covid but you must meet certain medical requirements for that such as fever, oxygen levels defined over a set period. You could check Nomad type insurance that covers for most countries if you are travelling around but again most policies likely don't cover for quarantine costs.
Where are you in Thailand? And what is the purpose of Non O (it's non O when you apply in Thailand)? If you are visa exempt or tourist visa you can convert to non O. In Phuket you must do so with min. 21 days left on stamp. Think it may be less in other regions. Must have 800,000 in Thai bank at time of application. This is a 90 day then when 30 remaining must apply for retirement extension (if that's purpose of Non O) money must sit for this time and this level maintained for certain time periods at start and when renewing. Send me message if you want more details. Age 50+ for retirement.
Check your passport stamp. If you arrived without a visa - visa exempt it is 30 days for Canadian and US citizens and you can extend 30 days. You need a photocopy of passport main page, page with stamp from your arrival and the departure card in addition 4cm x 6cm photo and filled out TM.7 form. Cost is 1,900 baht.