Having an indoor range is such a luxury and affords you the ability to get your zero dead nuts on which is extremely important. as far as moderator affecting accuracy goes my take is every moderator is different in mass which changes the harmonics of the barrel. Don’t discount a moderator and think it negatively affects your accuracy without fine tuning with that moderator on, I’m confident with some fine tuning you can get your guns to shoot accurately with any quality moderator.
My recommendation is to add Ernest’s carbon sleeve with 2part epoxy which helps a lot with harmonics, I don’t like FX carbon liners because they are too tight so any issue with how straight the machined tunnel/bore will be forced on the barrel. Ernest’s liners are just loose enough to allow epoxy to cure with no tension from the liner to the barrel. Just my opinion though. You can go a step either and get the full length carbon tension sleeve for the STX barrel which helps even more but a little less obvious after the liner sleeve.
Also how much tension you put when tightening the moderator on to the barrel also causes minor harmonics deviations so a lot of people just leave them on and get a longer case. Quite literally anything that change on the gun including taking off and on a moderator could warrant revalidation of your tune and very likely needs some fine tuning and definitely need to re-zero. But if you have both the carbon liner sleeve and carbon barrel tensioner then it’s much less likely. Once you get the gun to shoot dead nuts accurate then definitely leave it alone…..unlike people like me who likes to mess up a good thing.