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According to Quickload a 5 inch barrel is sufficient to push a 220 grain Matchking up t0 1050 fps with 44,000 psi loads. A suitable powder would be something like VV-N110 (11grains) or IMR 4227) 12 grains) to achieve 1050 fps. I'm not saying that would be practical in a AR-15. These loads have more energy than more common subsonic loads. They are less efficient with more muzzle blast. Muzzle pressure would be like like a supersonic carbine using modern cartridge, around 15,000 psi. Id want to use a suppressor made for a supersonic 308. The pressure would be as high but it's still a lot less propellant gas.
I chose 10.5" for my 300 Whipser pistols. That's the position where bore pressure and barrel friction become about equal giving minimum energy loads to achieve 1050 fps. I'd expect though that a 7.5" barrel could be made to work OK without much difficulty. . I haven't tried a barrel shorter than 10.5" Part of my decision was that I could shorten the barrel if I didn't like it, but I couldn't lengthen it.
A longer barrel will likely have greater velocity dispersion as bore friction not uniform from shot to shot, at least more variable than the energy from carefully weighed propellant.
A shorter barrel will have higher muzzle pressure and require more propellant, making a more difficult task for the suppressor. For a compact suppressed rifle consider the design by the company called "Refex Suppressors" made in Finland. The main expansion chamber is behind the muzzle and surrounds the barrel back to the receiver. They only extend a few inches beyond the muzzle.
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