Where are they?
The paper linked to above is a good place to begin, but it's only the tip of the iceberg. I know there is a lot of interesting stuff at the following places:
1. Aichi University online parabaik collection
2. Toyo Bunko microfilms
3. National library microfilms
4. The British Library
There are many other places as Tilman Frasch's "A Preliminary Survey of Burmese Manuscripts in Great Britain and Ireland" in the SOAS Bulletin of Burma Research shows. The history behind editing and publishing editions of important chronicles like U Kala, Hmannan, and Toungoo during the colonial era is also worth investigating.
Of course, the only reason I know about these primary sources in the first place is because I read books by professor Victor Lieberman like Strange Parallels: Southeast Asia in Global Context, c. 800–1830, Volume 1, Integration on the Mainland.