Get some high-strength Locktite or Permatex ). One is called Sleeve Retainer and the other Stud and Bearing Mount, but they're the same stuff, regardless of color.
Take a fired case, or pull the bullet from a new one, preferably a CCI, due to rim thickess. If you don't have any shim stock, take an aluminum (soda) can and cut a shim to glue to the rear of the case.
Remove the screw and pull out the barrel, clean all surfaces and apply rubbing alcohol or other degreaser. Then, reinstall with high-strength Locktite. Use the case, with the added shim as a Go-Gauge and if the joint is loose, the screw can help align it, but in any case, be sure the barrel is aligned with the receiver.
The screw is optional, but install it if you don't trust that the Locktite is better than the screw (it really is).
Loctite can be removed with heat that's not high enough to damage steel.
I've used this method of installing barrels on several rifles, mostly 10-22s. It's never failed.
Picher