Winchester WLR primers are magnum primers, so I have to wonder why only those were used.
I don't know if you can find CCI #34's, but they are magnum rifle primers. And the cup is thicker. The military wants primers that will make the cartridge go bang at minus 40 F, so military primers have been magnum primers.
Around 1999-2000 Winchester went to the brass finish rifle primer. What Winchester did in that product change was make the primers more sensitive by thinning the cup. Loads in my AR15 that had no problem with nickel plated WSR pierced constantly with brass WSR. That dished the tips of my firing pins, which required replacement. When you are shooting a magnum round, be aware of this. Firing pins in AR15's are about $20.00, your bolt gun firing pin will probably cost $200 to replace. Or at least don't be surprised at a crotch grabbing replacement price!
If you want to use magnum primers, look for CCI. CCI cups seem to be thicker than Winchester. Don’t ignore Federal primers, they work just fine.