Good old Bullseye Powder is nice and fast, and can be used clear up to 44Mag... It should be able to power a 55 grain chunk of lead down a 10.5 “ barrel and be completely burnt before the lead leaves the barrel.... Start out using a tame 9mm loading, using small Rifle Primers, and then build up to the accuracy loadings you desire...
You could use bullseye in 5.56 but you could only use a few grains. I doubt it would cycle a gas operated gun and there would be so much empty volume in the case they would never fire off consistently. At least with RE7 I think it would fill the case around half way so they would likely fire off consistently and I would expect it to cycle a gun.