Many of the things mentioned here will be helpful and predictable. Faster powders normally produce less muzzle pressure, burn more completely and have less flash. Those are all considerations. Some powders are just plain loud. Anyone who shoots Hodgdon loudshot in a pistol will attest to that.
Generally speaking, reducing a load using a loud powder will only make it worse. You lower the burn rate, have more unburned powder, and more muzzle pressure. If anything you want to increase the charge or seating depth.
Since you’re not shooting subs, you want the most efficient/complete burn at the lowest muzzle pressure. This gives the suppressor less gas and sound to mitigate.
At the back end at the ejection port you want to delay the unlocking of the bolt as long as possible, and limit the excess gas. If the system wasn’t over gassed the begin with, it will be with the suppressor atratched. An adjustable block turned down to minimum needed for the bolt to lock will make a noticeable difference.
LMT makes an enhanced carrier that has a lengthened cam path that delays unlocking, it makes a noticeable difference in sound at the shooters ear. It also makes shooting an AR a bit less hard on the brass, it had more time to cool and shrink in the chamber before extraction.
Plenty of things you can do after finding a better powder, but a loud powder can’t be helped much.
I don’t shoot 223 so can’t give a recommendation, but the principles will hold true for any cartridge.
Thanks for the reply. Good points, I think. I realized, as I'd posted a few days ago, that I'd stepped off on the wrong foot after the first few replies came in. Your post only makes me more convinced I'd stepped off in it.

I think the consensus is that the H335 powder is a poor choice, which is in-tune with your statement about "loud powders". Your statement about the gas/sound to mitigate is understood. I tuned the gas with the suppressor attached (you're right, the addition of the suppressor makes a bigger difference than I would have thought before I ever had a suppressor).
I'm going to look up the carrier you mentioned. As one other responder mentioned, heavier buffer/spring combinations will delay unlock and help to mitigate the noise at the port. That's two votes for delaying unlocking of the bolt. I currently have both a JP SCS H2 and a Tubb's flat wire available. A traditional H2 buffer and the flat wire or the SCS H2 can be tested fairly easily. I've got some ideas (of my own and from these responses here) for loads I'd like to try first, though.
Thanks again.
--HC