What are the options for extending a 45-day visa in Thailand to stay until March?

Okay, let's see if we can get this sorted out. First let's take the "we want to stay until" out of the equation and see how long you CAN stay here until. 😮

You came in on a 45 day visa exempt entry, that runs out on Oct 22, you can get ONE 30 day extension (which will take you to Nov 21) and then as you correctly stated you could then apply for a 60 day covid extension which takes you to the end of January. <- That's the maximum you can stay (whether you want to stay longer or not 😕 ) as things are now.

All you can do is keep with that plan and watch to see if/when the covid extension is continued or not,

OR

whether the borders open back up allowing you to exit/re-enter and start over with a new visa exempt entry stamp

You probably have a Visa Exempt stamp in your passport rather than a visa on arrival which cannot be extended.

You say WE...

WHO IS WE?

Passport nation?