How long must I leave Thailand after my DTV visa extension to re-enter and stay again?

First of all, give up on any idea of extending the DTV. It's almost impossible and even if you do manage to do it, you'll have to take so many trips to immigration and spend so much time in the attempt, that you won't even bother next time.

Just do a border bounce when you need more days. You're not required to spend any amount of time out of the country. You can cross a land border, turn around, and re-enter immediately for a new 180 day stamp. You can fly back same day if you can find a flight schedule that works.