I thought a TM30 was always required for extension, just that they usually are already in the system unless you have moved provinces. Was I misinformed?
Have you thought about visiting a nearby country for a few days? If you get the 60 day visa, then extension, that gives you 90 days in country. Then go visit Singapore or Malaysia, or anywhere for a few days, then come back to Thailand on exemption.
You SHOULD be fine to do that. Might get dodgy if you try more without actually moving around Thailand as well.