I dunno about the cab, man...I have 3 cabs...Mesa halfback metal grill 412 loaded with legend V12s, Fender MH412 loaded with Legend V12s and Mesa V30s, Avatar Signature 212 loaded with Legend V12s. I play all of my cabs at high volumes these days, and there is never an issue with getting enough gain unless a preamp tube is out, or, in my case, something was wrong with the amp...which for me was blown orange drops throughout the amp, apparently lol.
And I also agree that this amp should have a SHIIIIITload of gain. You shouldn't be having any gain issues with the amp itself, and I really doubt the cab is causing this problem. By all accounts, your Mills should be equal or better than my Avatar.
My IV would lose gain, sustain, and volume, and just generally sound like shit when the OD caps were bad. Once those were replaced, no issues.
I did have a bad preamp tube that reduced gain and volume when I cranked the volume up on the amp, but that was easy to fix.
Is your amp still covered by Mesa's warranty? If so, send that bish in and get it looked at.