How can I extend my 30-day visa exemption in Thailand for an additional two months?

Kyle you don't say where you and whether your current 30 day exemption was by land but it's worth bearing in mind that your limit of 2 land visa exempt entries resets on 31 December and we are in the second half of September anyway so if you haven't entered already this year by land, you can get as much as 4 months out of just doing land visa exempt runs with extensions and that gets you through to January when it resets so you could do another four months there bringing you as far as early May... all on visa exempt land border runs... theoretically.

You should have bit the bullet and just bought the 6 month METV in the UK

you can go get a 30 day extension on this visa exempt stamp for 1900baht at the immigration office

Then you can go to a land border, stamp out, stamp in&out of another country and stamp back into thailand to get a 30 day visa exempt entry, although you're limited to just TWO of those in a calendar year.