I don't know how much experience you have with trying to run sub-sonic loads, but from what I've found with my LAR-8 in 308, getting a sub-sonic load to cycle in a gas gun is going to be next to impossible. I run a 180 grain round nose (round nose to keep the length down so the likelyhood of a baffle strike is minimized) bullet in a 1/10 twist 308 barrel with around 10gr of Trailboss. It's very quiet, and a cool demonstration for friends to show how quiet it is, but it turns my LAR into a single shot. Doesn't come close to cycling the action.
In order to keep your velocity below 1000 fps, the bullet will have to be very heavy. I have a Noveske adjustable gas block on my 18" AR-15 and trying to get a heavy enough bullet with a fast enough twist to avoid a baffle strike is dicey at best. I imagine if you run a 10" or less barrel with Trailboss powder and a 80 plus grain bullet, you may stay below 1000fps, but I highly doubt it will cycle the action, regardless of how big you drill out the gas port. It seems to me that you're going to be risking a baffle strike and ruining a perfectly good suppressor, as well as having a barrel that has been drilled out and is no use for normal ammo.
The 5.56 is not a good option for sub-sonic ammo and I'd do a lot more research somewhere other than a board like this for a solution for the work you want done.