Don´t worry it shouldn´t be a problem sleeping in a tent or monastery. Usually the local authorities are ok if you contact them.
I met a guy who was doing this regularly.

I only got back from Myanmar not having a tent and I regretted not having one. It would have been so much easier.
Enjoy your trip, the people ar lovely.

If you need a friendly private place in Yangon (Normal price 20 but negotiable 15 or even 10 ) let me know.