I see no point in a Valkyrie bolt gun. The whole point of the round is to run heavy bullets at AR mag length. Bolt guns don't suffer that issue because even the 223 mags have enough to to seat the heavies out.
224 Valkyrie vs 223 Rem performance is negligible, 223AI will out perform it. If available components are a major deciding factor nothing is as available as 223 ammo and brass. Buy excellent quality fully prep'd brass from Precision Brass Ops, fire it once, and leave it on the ground... Or save it and reload it if you don't mind the extra work.
I LOVE my Valkyrie gas gun, but there's no way I'd build a bolt gun in it. It just doesn't do anything that 223 doesn't with a lot cheaper and more available components.