My formula for consistency, first off, is to use only two amp blocks - a clean amp, and a dirty amp, and to make them global blocks. The same could be accomplished with a single global clean-ish amp, and maybe a global drive block for dirt. Anyway, start with consistency across patches. I also find that using a guitar cab helps to constrain the parameters, so to speak. I want the guitar-in-room sound and I don't run FRFR to DI to the house. I'm currently running a VOX 2x12 with the Celestion/Vox Neodog neodymium speakers and I've been really happy with that cab. It's amazingly light - one hand carry! The Neodog speakers have a really nice upper-end smoothness that helps control some of the potential "hi-fi" nature of the Axe. That's not a put-down towards the Axe, it's just that it has the ability to produce/reproduce all the high-end you throw at it, and more, and it's easy to have a bit too much of that pop out and bite you. The right guitar speaker can help tame that. Though I imaging the same can be said for the right cab block in a FRFR situation.
Next, my sound got even more consistent when I switched to a Matrix power amp. You'll find others mentioning this as well. I thought it'd be a compromise giving up my Fryette/VHT 2/90/2, but in all honesty, the Matrix sounds better. Yes, better. Not almost as good, but better. People seem fond of comparisons between the Matrix and the VHT and making statements like "the Matrix sounds 95% as good as the VHT". I think that many of us still cling to the idea that tubes just must sound better than solid state; it'd heresy to say otherwise! heh. I still have to remind myself to not cling to that outdated belief that tubes automatically mean it sounds good, or that solid-state means it can't sound good.
What I discovered is that out of the box the Matrix gave me much greater "punch", or transient response, a tighter sound (maybe better phase response?), a more predictable high-end response - essentially less "fizz" when cranked, and an overall more controlled frequency response across the board. The response of the Matrix has enabled me to really dial in my sound, consistently, and dial in whatever amount of sag, fizziness, and other non-linearities I want by taking advantage of the power-amp section of the amp block. In fact, I thought I'd miss the depth and presence controls on the VHT for some on-the-fly adjustment, but I've found that the Matrix is so much more sonically consistent than the VHT that I don't miss those controls.
Not saying the Matrix is the magic bullet, but it was the right move for my rig.