What are the options to extend a visa in Thailand after a COVID extension without leaving the country?

You can get unlimited Covid extensions as long as the program is still running.

Right now the last day to apply is January 25th. We won't know if they continue the program until probably the 20th at the earliest, more likely the 23rd or 24th.

With that said, the extension is at the discretion of the immigration officer so it's not guaranteed. But try before you resort to some other option.