Re: .22 thru a .223
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Precisely put, its the last thing one would want to do, but in limited practice with the right .22 ammo, it can be done.
With sealed suppressors "one only gets out of them what one puts through them" shoot clean burning, high quality .22 powder with plated (copper) .22 bullets and the resulting leading and particulate is minimized. Shoot crappy cheap ammo with unplated .22 bullets and do it a lot and your can will take on the kind of fill that thousands of rounds of .223 could not duplicate.
Some will argue, some will point to the fact that they have done exactly that, poor ammo / high volume, for prolong periods with little effect. Others will say that a couple of .223 and its back in business. This would help with the particulate and never touch the leading. As your is a bolt gun, you have spared the gas system.
If it was me? I would look for a good .22 can and have at it.