Compensator diameter is smaller than barrel diameter

[Shazmataz]

I just got a new rifle with a 1.1 inch barrel diameter but the compensator I got for it (needed for my suppressor) has diameter of only .85" so there is a kind of lip on the end of the barrel that I don't want exposed, if that makes sense. Is there any way I could get a shim or something with a diameter of 1.1-1.2" to cover the end of the exposed barrel.
I will post some pictures when I can. I've been looking for solutions to this for a few days and got nowhere so any help would be greatly appreciated, thanks

(Also, sorry if this is in the wrong area or a repeat post)

 

[Shazmataz]

If you can see in the first two pictures there is a slight lip where the compensator meets the barrel I want to do something to this so that isn't showing so much and something that if the barrel gets hit in that area that edge won't take the brunt of it. Any help is greatly appreciated.