I am somewhat of a trouble shooter by nature and job. You have to figure out, what is it in the chain that is holding your tone back".
Ok lets recap. You have an AXE-ART SLA-CAB. Well we all know the Axe works for most. And your Cab is fine because you play other amps with it. So Obviously it would be in your best interest to try another power amp, or try to use a different amp head instead of a power amp. I use a power amp too, but my friend goes into his Marshall Head with the front input and the fx loop and he gets a GREAT tone too !
So maybe your ART and Axe aren't friends ? Maybe something is wrong with AXE or ART itself? (a tech would know).
The only way to rule out the AXE FX is to plug it into multiple heads or amps and then see how it sounds. If all the amps you try sound bad, get your AXE serviced. If another amp gives you that tone you want, think about not using the ART with the AXE anymore. However, from what I read on these forums, people love their ART /AXE relationships.
When I plug in my Axe to my Fryette 50:50 I don't even really need to tweak. I picked the 50 presets and user presets that sound great ! Also, stick to modelers that sound like the other amps you are using as your ear is most likely NOT DEAFENED, but you are "USED TO" hearing a certain tone from your other marshalls.
It will happen, hang in there, and rework it !
...please excuse me if you have already wrote that you did all this, and I just missed it in the previous posts.