How are you getting the signal to your monitors? Direct or through a computer?
The demos of stock presets don't sound too different from what I would expect. But the compensation in EQ in the later demos sounds like it's overcompensating for your listening environment. The demos did sound quiet. I'm not sure what setting you have the volume. Could be an element. Possibly not. And I'm not even sure about the listening environment part.
However, I dislike the Orange models for exactly the reason you're here. I imagine the cab blocks are a large portion of the culprit. I'd recommend staying away from them.
I don't really want to type out a huge wall here, but (EDIT: here I go apparently) my recommendation is to look at the internal routing like an actual tube situation. (Also, before I continue, I want to point out that I strongly disagree with your statement that minor EQ can compensate for a muddy guitar/pickup. Sound starts there. Pots, pickups, material. Huge impact.) I rarely go to these high gain amp models for my high gain tones. I'm a bit of a different player, but look back at some of the great high gain pioneers. Also, you might think you need more gain than you really do, but that's a different conversation and I don't want to seem like I'm patronizing you.
I am personally getting very good higher gain results with more classic amps. I think it might benefit you to explore that realm for multiple reasons. One, it'll simplify some of the structure. Going with an amp that "doesn't have" a master volume simplifies the gain sounds. Knowing the difference between preamp and power amp distortion is a good lesson. It can really guide you to how you want to push your amp.
But I want to take one step back with that in mind. Going back to a more classic amp, get a good clean tone. One that sparkles in the way you want. Lush, but not boomy. Then start to push the amp from there. I'm not a huge fan of TS style pedals, but they play their place in tone shaping. They cut some lows and really notch out your tone. I'd recommend a Centaur for a flatter type of drive to push the tone toward what you want. Then pushing the drive on your "masterless" model to continue. An alternative to the drive on the amp could be as simple as a clean boost (EDIT: Clean boost could be as simple as a flat EQ with up to 12db of gain across the board. Or +6 to the mid section and +12 to the highs on the Simple EQ) to slam the front end of the amp. You'll get some nice play with the harmonics going on.
I also suggest (if I haven't already. It appears I'm writing exactly as much as I didn't want to.) from there to start playing with the mics and their placement. Start with just one cab. One mic. It'll isolate the variables in the rig and you can grow from there. You'll be better for it. At least it's good for me, anyway.
It really helps to have some good tube amp experience to guide you through. It really informs you on what kind of beast you're dealing with. For instance, I don't particularly care for Rectifiers for their muddiness indeed. So that's already one step toward what your problem is. I experienced muddiness with most of the high gain models. 5150 might be closer to the bite you're looking for. I am personally having a lot of success with the Bassman. I visit other amps like the AC30 (fawn or not, one of the most capable amps of all time) from time to time, but I keep going back. Then again, I go between rock/metal to blues/jazz, so it's a nice little setup for me.
Just recently though, I've changed the stock cab with the mic six or so inches away and some early reflection to a blackback with an 84 condenser up close. I wasn't liking some low end flub that was happening, so I tightened it up in a 412. This is all to say that there are options. And it's not all necessarily EQ. There are so many characteristics to explore that EQ just won't solve.
In conclusion, I'd say take a look at your pickups (I'm not particularly familiar with yours). And take a look at how you're feeding your signal to your monitors. I imagine it's going through your computer somehow. Could be your interface. Maybe there's some knob turned on your digital "console." If it's not a matter of a dark guitar or a monitoring signal path snafu, take a look at how you're creating your tone. EQ should be a last resort. If you can master edge of breakup tone, you can easily step into the high gain world from there with all the bite and nuance you've ever desired. That's what edge of breakup is all about.
Now that my dissertation is done, I've been inspired to go mess with the Helix. This thing is really great. I've learned even more because of it. Mostly about cabs and mics, and how they react in a space. It really is a guitar studio in a box.
