As part of the testing that led up to the development of the 7.62x51, a number of guns, including BARs and M1919s, were converted to the various prototype cartridges to test their feeding ability.
Supposedly, a number were even converted to Ground Zero -- .300 Savage.
As far as M1919s in 8mm Mauser, I'm pretty sure that several hundred that were given to Israel during the early days of that State's existence were converted to 8x57 and used in various conflicts.
And hey, look at this!
A Utoob how to guide on converting an M1919A4 to 8mm Mauser.
http://www.youtube.com/watch?v=vzTSHhW9Wg0
Neat!