I have one and they certainly are tricky to get right. First, what power amp do you have, as SFW said, they do surprisingly play a big role in the sound. For my settings, I started with Petrucci's and tweaked from there. Actually, his tour rig from 2015 or 2014, he used the Triaxis again. You can get a screen capture of his rhythm tone (which is lead 2 red) and use the eq's as a baseline also, as they are different than the 1993 settings online. As you have probably learned, Ld2 is where it is at, and the eq changes to that mode, don't really make much difference across the yellow,green, and red settings. It's more about the squishiness or edge that those three 'color's changes to my ears.
I prefer green over yellow, but they are pretty interchangeable really. John's most recent settings are: 8.0 6.0 4.5 3.0 0.0 6.5 5.0 3.5 3.5. LD2, Red. This is his rhythm sound and it is tight and focused. When played loud, with my mesa 50/50, it is his rhythm tone. I used that as a basis to revamp my lead tone, by changing it to LD2 Green or Yellow and up the Drive setting to 8.0 and the DV at 3.0. The key is to not have the dynamic voice too high, or it injects gain into the signal. Also, everything along the way seems to add bass or woofiness, so you have to keep that dialed back (anything more than 4.0 in my experience is a mushy bass mess). Some settings that I've found online had the DV higher, with the bass at 0.0, that still had a huge amount of low end. Also, I run the outputs (rotary knobs) at 1:00 o'clock and I only use the loop for a rack compressor like John did on the I&W tour for the clean sounds.
As a last note, I have had my rig since 1999. I left it at a friends house for a few years while he remodeled. When I got it back, even though it was racked and the rack covers were on, it was covered in dry wall dust. The sound was different, lifeless, woofy. I was pretty pissed to be honest, that he didn't cover it at least. I changed the preamp tubes and the power amp tubes, but it still sounded different. As a last resort, I pulled up all of the manuals again, (triaxis, and 50/50) and went through and reset all of my settings (which is why I found John's new settings). What I discovered is, that my power amp has preamp tubes inside it. I changed those out and holy shit, that opened it right up. The presence was back, the definition, the tone. So, if you haven't changed tubes in a while, you might also want to consider that as well.