You want to know how to reign in the dominance of Rebel Jankyard and similar Biggs/Lowhrick/Rex lists?
Give Imperials access to the Arc Caster. Seriously.
Vessery with TIE/D, Arc Caster+Ruthlessness could and would be a serious threat to these types of lists. And even though he wouldn't be great against other lists, he's still TIE/D Vessery- he can still pull his weight! Plus there's some neat strategies for synergy with other ships- notably Quickdraw. Imagine Expertise/ArcCaster Vessery and QD fly into range 1 of a target. QD fires his attack as normal, getting a TL from FCS. Next, Vessery Fires fully modded Arc Caster, hits, and puts the splash damage onto QD- triggering his pilot ability attack, full mods. Then Vessery follows up with his primary, full mods. In total, that's 16 red dice, 12 fully modded (assuming QD has Expertise too). I'm not saying it would be top shelf, but **** it would be fun- and you'd have to fly aggressive. Plus the Arc already has a balance feature in it- the fact that it has to recharge, so it's not like you could do this 2 turns in a row.
Combine that with the fact that the Arc Caster was designed and built by the Empire (see SW: Battlefront), and I think it gives a viable option to counter lists like this. If only the Devs could get over their irrational hatred of Imps, we might be able to balance this game!
STOP THE DISCRIMINATION AGAINST THE IMPERIAL FACTION! FREE THE ARC CASTER!