@Megan *******
, as you can see there is more than one way to achieve your goal.
The easiest and least troublesome would be to get a SETV <- single entry tourist visa from a thai consulate in your country BEFORE you wing your way here. That would get you stamped in for 60 days when you arrive.
Then after those 2 months are up go see some countries in S/E Asia like you intend to
AND
then just BEFORE you intend to come back to thailand get a single entry tourist visa from a thai consulate in what ever country you're in at the time. That will also get you stamped into thailand for 60 days when you come back.
That is the easiest, least troublesome way to pull it off. It doesn't involve bouncing out and back in at a border, it doesn't involve dealing with ANY immigration office inside the country and it meets the criteria you said you wanted.
Good Luck