From the Accurate Powder Reloader's guide, using Solo 1250 powder, which is a fast-burning shotgun powder:
55gr Fmj 3.5gr S1250 1139fps 13500 PSI
Hdy 60gr SP 4.2Gr S1250 1111fps 19100PSI
Hdy 75grHPBT 4.5gr S1250 1052fps 22100PSI
You will need some "stuffing" (e.g. cotton lightly packed) on top of the powder to keep it in place.
I haven't tried this before w/.223, but have loaded subsonic .308's -- 168 gr. match bullets at ~1000 f/s using a medium-speed pistol powder (Accurate #7) for father-in-law's long-barreled (24") Ruger #1SS.
Theory was he wanted to nail some deer on his property in semi-rural Maine shooting from the barn, but do it quietly so as not to disturb squeamish neighbors. I rigged up a "supressor": a four-foot long 12" cardboard tube for concrete footings, lined with foam. We set this up on sawhorses, and he fired the rifle through it. Between the long barrel (which let the powder burn quite completely), the "suppressor", shooting from within the barn enclosure, and a subsonic bullet, it was amazingly quiet. Sounded basically like him doing some heavy hammering in the barn, and printed 3 rounds cloverleafed at ~75 yds (the distance to the apple tree where the critters dined).
Filled his tag on his own property that year.
I've always thought a subsonic heavy (>62 gr) .22 would be good for turkey in noise-sensitive areas. Load development does take time, and you do have the alternative of the Aguila 60gr SSS in .22LR. I have not gotten the Aguila to shoot well from standard .22LR barrels (vintage Anschutz M54 Sporter), probably because of the slow 1:14 twist. The Aguila needs 1:10 or better, IMO. I understand you can buy 1:9 barrels for 10/22 to turn them into dedicated SSS guns. The SSS is very quiet from my M54; again the longer barrel helps.
Good luck. You will learn a ton from the project, so have fun with it. Don't be swayed by arguments it's not "practical". Neither is most of the stuff we do in this hobby.
[ed. for spelling]