I'll just repeat the same thing I've been saying: The main thing I want out of such an overhaul is for player damage to stop going out of control so easily. The damage upgrades are just too good. Right now in my build of the game Terminus has a grand total of 26000 HP, before damage scaling. That's a whole heck of a lot. But it doesn't help much... even with a build that's just not very focused on damage (sorta being a bit more all around) it still ends the fight way too fast. For the final form, which has 7600 HP and is meant to be an attrition phase, the full threat of the pattern didn't even have time to form. That's a bit silly. This is with the purple mech, mind you, and I still had it's mines at the end. So no energy weapon really adding damage. But a high-ish fire rate, some of the big damage perks, and a decent amount of crit still melted it.
And of course the side effect is that the damage perks are so freaking good that they just seem objectively better than everything else (other than the shield one), so nobody takes anything else.
Some damage-up items may also be contributing to this, too, I'm not sure.
Now, feedback on the other ideas:
Damage splitting: Best not to. It ends up meaning that many energy weapons would be overall useless later in the game; players are very likely to end up focusing mostly on basic attacks more than energy attacks. I definitely think that simply toning down the amount of boosts from the current buffs is the way to go. The numbers on those are just way too high and you can get a whole bunch of them if you want (but you don't need that many to do it, really). Energy cap upgrades already serve a boosting purpose for those weapons anyway: the higher the max is, the more damage per room you can do with any given energy weapon. It's already very possible to do energy-focused builds; while many players don't seem to do this, it can still be very powerful simply from increasing the max by a whole bunch, depending on your weapons.
Trap Master: Just giving immunity to EVERYTHING at once is way too much. However, if there was one that gave immunity to spikes, and another that gave immunity to lasers, those would both be perks I'd definitely consider taking when they appeared. They wouldn't totally nullify the non-enemy challenge of rooms, but they'd still be very useful.
Keyprentice: I like this one.
Shard efficiency: I like this one too. It takes quite a bit of shards to get more HP but basically everyone seems to collect them obsessively. So it's useful in most playstyles.
Missile pack: That sounds like a good change.
Armor upgrade: Hmm, not a bad idea, though it'd need some major testing.
Extra XP: Don't we already have this?
Auxillary system: This sounds pretty good. Though, we do already have an anti-death perk, the one that simply revives you at the start of the level with full HP (without requiring that you be holding a module). But more creative ideas would be interesting. Sounds a lot like Lazarus in Isaac.
Specialist: This sounds good too, though high bonuses to basic attacks are still going to make things messy.
Debuffs: Now this one sounds pretty entertaining. However, the chance of it happening would have to be incredibly small, considering how many shots the player is capable of firing. Why not have this one be tied to missiles instead? Guaranteed to work with missiles every time.... the cost of course being that you'll run out if it's overused. And some enemies are hard to hit with missiles, though of course you can get special launchers to remedy that.
Piercing chance: Too weak. Enemies really don't tend to clump up much aside from the new Popcorn types.
Culling Strike: This could be pretty good against some things. An anti-Fearsome sort of thing, and those are the enemies that get players panicking more than anything. Bosses & minibosses should have immunity to something like this though. Actually they should probably have immunity to a number of things. We do already have an anti-boss drone.
As for existing perks, the one that gives a 40% chance of doubled credits seems a bit too strong to me. I'm sure I can think of others but that's one that comes to mind. And of course all of the damage ones.
Also having mechs with more unique perk setups is a great idea. Right now they really are a bit samey when it comes to that, which isn't very interesting. Having each one stick with more of a theme would be nice. And of course some perks that are entirely unique to each mech is a great idea.
All of this is sounding like it's going to be another really nice update to the game here.