The IRs from my Hard Truckers cabinets are here:http://playingdead.net/vic/
E-120 is a 2X12 loaded with E-120s; the K-110 is a 2X10 with K-110s ... guess that's obvious.
If your controller is able to change patches, that's also being done with a CC message, so you might look further into programming the buttons on it. Or remapping the AxeFX to use whatever messages it is sending by default.
On the reverb, I have the reverb block set to 100 percent wet, and use very little of it in the final output, so the reverb itself is crispier but it makes very little difference to the sound of the guitar as shaped by the JBL IR files. The only part of the sound getting around the IR is the reverb itself.
The K12s have served me well; another option is EV's new ZLX powered monitors, they look good and half the price of the QSC. I have a pair here but haven't tried them out yet.
Having set up my old analog rig side by side in my studio with the AxeFX and K12s to dial it in, I would be very surprised if you can get them to sound as "in the room" as you want them to. When you turn it up through the powered monitors, the sound is bouncing all over the place just as it does with a real amp. Very little difference to my ears.
The key to getting it dialed in realistically is not to let it be too crispy sounding. Pay attention to the response curve of the actual JBLs. One of the first things I did was put a low pass filter on the amp block to cut down high frequencies above 7 kHz or so. That being said, Garcia's guitar is quite bright when you hear it isolated. It's just not a lot of brightness above 7kHz in the real world because the speakers didn't pass it. It's my belief that the reason the 94-95 tone is so bright and acoustic sounding is because he was not using a speaker simulator and just passing all that information into the PA -- it probably cut well over the in-ear monitors and his high-frequency hearing was probably shot at that point anyway.
Pay attention to how your guitar sounds in the overall mix of the band, not how it sounds alone in your room ... that is the most important thing.