That .30 Mauser didn't generate nearly the the pressure of a .250-3000, Joe.
An AR-10 in .22HP? Just go with an AR .223- pretty nearly the same performance.
As for re-barreling a 99, having a new barrel threaded, fitted, chambered would probably run more than sending the gun out and having it re-bored to a larger caliber.
Have you shot this rifle? Sometimes nasty bores can surprise you with how well they shoot.