Cranking the lows up to 2 o clock is actually a pretty good amount of boost. What kind of bass are you using?
I would say if the sound guy is telling you you're too loud, but you can't hear yourself, the answer is not to go to a smaller cab, but to make the one you have work better for you. You could try raising it up, or angling it back. You could try standing further out in front of it. You could experiment with adding more mids and/or highs. In other words things that get more sound to your ears, without necessarily being "louder" in the room. You could also experiment with adding a bit of tube overdrive, which with the right EQ curve can sometimes make a bass sit better in a mix. Especially for a classic hard rock tribute, you have a fair amount of leeway with that kind of stuff. Just don't overdo it or you'll make the bass muddy/spongy which is the opposite of what you want.
But I will also say, it could actually be the reverse. The sound guy is out front directly in front of your cab, getting all the mids and highs which you have set flat, PLUS a lot of bass, and that is contributing to a "too loud" perception. You could go the other way with lows set flat, and then do a modest low mid cut and possibly a deeper high mid cut. The high mid cut keeps the bass from sounding too harsh or aggressive, and the low mid cut makes more space for the guitars and drums (ie snare and toms). The key is to not overdo it. So if you dial in the cuts like that while playing solo, back them off a bit (less cut), and then you will likely be right where you need to be.
And yeah, the other thing about the GIII is figuring out a way to make moving it easier. Mine has casters, which I wouldn't be without. Even if yours doesn't and you can't find the right ones, you can probably just get a cheap small furniture dolly to move it around on. In the states, there's a company called Harbor Freight that has all kinds of stuff like that, I've bought a number of the same small dolly (maybe 15-18" long and a foot wide) for about $12. So I think I have 3 or 4 of them now, because I use them for guitar combos and bass cabs and then keep at least one "free" for general usage. And damn, your bandmates should really help with load in/out. That's BS if they don't, as long as you're willing to also help them. At home, sure, you may have to just deal with it. But at the venue it really shouldn't be an issue.
For now, if you gig the Jr, especially since it's 4 ohms, I would definitely get it raised up on something, so that every watt you put into it goes straight to your ears. And you may have to ask the sound guy to put a little bass in the wedge. The idea is not to get blasted with bass, because unless you're dealing with old school giant 15" wedges, they're not really designed for that. But just to fold in a little bit, so you have some definition. People try to just add everything to their monitors and that is the complete wrong way. You only want to add what you absolutely need, and if one thing on stage is way too loud and causing you to need everything else, the one loud things needs to come down instead.