I read through the description on the EL34II and the EL34L. If you opt to change to the EL34II, get a mental image of the STR447 in your head and listen to the note definition at a moderate gain setting, say at noon or 2pm (crunch and crush).
As for the 6L6GC tube being hotter, I would agree. The BAD relies on that power tube distortion more than you would think it does. It is not a Rectifier in the sense of the Dual Rec Roadster (need more headroom tube or it will get muddy), The MWDR can run a hotter bias tube which is in the grey color. Green is basically middle of the road. The BAD runs well with the Greens but going hotter than that with the JJ 6L6GC may be over the top as it is a very aggressive sounding tube in all respects. I really like the Mesa STR445 (JJ 6L6GC) in the Badlander, with those tubes in the amp, crunch will have more usable gain than the crunch of the Mark VII. Crush is on par with the IV mode of the Mark VII or CH2/CH3 of the JP2C. If you want the grind of a IIC+ without forking out the high dollar to get one, the JJ 6L6GC is one way to get there with the Badlander.
When using the EL34 tubes, the sonic footprint is different. Crunch will sound closer to the rectifier and the crush will be more like the VII mode of the Mark 7. The perceptual gain will be less but still good in all its glory for that old school 60s-70s rock. Since I have a Mark VII, I will probably return the Bad to using the EL34 tubes which keeps it different.
EL34 or 6L6GC, the Bad has similar sonic qualities of the JP2C, meaning it retains note detail no matter how much gain you muster in the preamp. That to me is an edge over the Mark VII in all respects as the Mark VII does not seem to hold onto that characteristic unless you change the power tubes to a colder bias to compensate for the tube saturation you get with Simul-Class power output.
I would consider the standard ECC83s tubes vs the HG version or you may get tube ping when changing channels or worse, self oscillation (microphonic issues). I did try some higher gain 12AX7 tubes just for kicks, that made it more difficult to get to gig level without backing off on the gain since it would push the amp into uncontrolled feedback. Perhaps if they can offer the same grade of ECC83s as the one's Mesa uses. I never got around to trying the E83CC tubes in the Badlander yet. they are a bit different than the standard ECC83s tubes. Just keep in mind that the V2 and V4 have cathode follower circuits, V2 is that dc coupled cathode follower circuit common with the Rectifier amps and V4 just has the typical cathode follower circuit use for the FX send circuit. That leaves just V1 and V3 to mess with, it is basically a Mark lead drive circuit. Phase inverter is typical Mesa design so a match triode tube is needed. That can be HG if they recommend it. It may be fine to use all HG in the V1 and V3 as well. V3 has the triode circuits with the higher gain. This was based off of the tube task chart in the manual and after poking around the amp with a multimeter to find what the plate resistor and cathode resistors used in the preamp are. The Badlander is a hybrid, combination of the Mark lead drive circuit on the front end, followed by a traditional tone stack driver and FX circuit of a MWDR.
If they need the resistor values (measured with a multi-meter),
V1A plate: 100K, V1A cathode: 3k
V1B plate: 82.5k, V1B cathode :1.5k
V3A plate: 270k, V3A cathode: 3.3k
V3B plate: 130k, V3B cathode: 1.5k.