Feeding a BR ... check into Wyatt's center feed box. I believe it's only "two down" but to me that's better than a single shot.
Barrel life should fall between a .223 and a .22-250 if each is built with the same precision and used the same way. Heating one up but not the others throws the barrel life comparison out the window.
I think the ideal .22 BR would be built on a Remington XR100 or 40X single shot action. Maybe a Ruger #1. With apologies to Blazing Saddles ... "Feed? we don' need to steeenking feed."
Tom