Yeah, agree. It's a bit a no free lunch issue with regards to the performance constraints. Understand that the OP wants to approach this economically, and is wondering if there's a path.
But considering suppressability and performance for larger varmint size game, I think a larger payload helps. Something going 2000+ fps will be noisier than something going under 1100 fps. The 200+ grain 300 BLK round will have better terminal effects.
Subsonic 300 BLK zeroed at 100 drops 12 inches at 150 yards and quite a bit more thereafter, so that is a disadvantage if someone is keen to shoot 200-300 yards. However the accuracy of the bullets at 100 yard and greater differences is really excellent. By contrast, 22LR and 22WMR groups really open up in most platforms at 100 or greater yards. (realize that he's looking at 223 bullets which likely retain spin better even at slower speeds)
Don't disagree. But your thoughts have gone from 22 caliber to a jump to 30 caliber, which is why I don't disagree, especially with regard to the terminal end.
Where I'm scratching my head is with 22 caliber. I suppose that one could try to lob a 62 grain or heavier .224 pill out of a faster 7, 8 or 9 twist barrel. But then add the suppressor. Sounds like a good way to throw subsonic knuckleballs to me, and "why" really comes to mind first and foremost. But there's such a thing as "why not" too. Maybe I'm missing something?