Shouldn’t be any issues to re-enter on a 60 days visa exemption after you’ve stay in Thailand on extensions based on a Non O-A visa. You can apply for a 30 days extension, but you don’t get re-enter permit on visa exemptions. You’ll just re-enter on a new one.
Yes since 15th July, you get 60 days visa exemption instead of the old 30 days and still can do a 30 days local extension. So 90 days without visa if you wish.