Go with a .22 CHEEtah or .223 WSSM. Or why not trade for a less redundant bore? And choose a rechamber/custom job in a cartridge TOTALLY dissimilar to a .223 Remy, Swift, or any other .224? OTH, if your barrel was a bull, go for a rechamber/rebore to a .257 Bob or 6mm Remy.
If you must stay with a .224 cartridge, look long and hard at the .22 Bench Rest.