I have not found Tikkas to have enough meat for a shoulder when threading to 5/8-24 for most common 30 cal suppressors.
I have done about 5-6 T3s now and have pressed a shoulder behind the threads on all. I have done one .223 threaded at 1/2-28 and it had plenty of meat for a sufficient shoulder.
I would guess the "shoulder ring" is an interference fit?
If so, does it have a constriction in the bore beneath it?
I have not done a gage ball drop test but I highly doubt there is a constriction. The rifle still shoots 3 shot touching groups regularly. There was a very small shoulder after turning the area to be threaded to .625". If I recall about .020-.030 per side, so the ring has at least something to stop against. You don't need a major press fit. The ring is slip-light press fit with LocTite cylindrical bonding compound applied.
So the ideal process is to turn the muzzle OD to .625 for the proper length (desired thread length + length of shoulder ring), install shoulder, thread from muzzle to shoulder.