And I beat it all the way through Klyntar in one game today. So after playing it way too much the last few days, here's my strategy now:
The basic idea of stacking Mayhem and Carnage with both 2x exp modifiers is unbeatable. This easily gets up to 20 or more for level and nothing else comes close to doing that. I had said to do this with the flamethrower too, but the problem is that requires three hosts to set up, so you can't do it all on ball 1 (you're not going to reach and beat a boss to get a second host change without the levels from Mayhem.)
My plan now is start with Peter, fill his dots, then switch to Gwen and do Mayhem/Carnage with her as soon as you fill the 2x exp box. (You don't even need all six locks for Mayhem, just at least the three on the left.) This order is better than the reverse in order to have Gwen's 2x infected power during the stacked multiball, to push Doppelgangers and get Sleeper (10 infected) for Toxin Team-Up after.
Level 20-25 is high enough to go for Phage while still on Gwen. If you lose (not by draining), just keep going on Gwen and try again, you want to regain that 2x exp box. If you win, change to Eddie next. If you lose by draining, pick Flash next.
The tricky part now is navigating around Flash, since Agony almost always gets beaten during Mayhem, and if you switch to Flash then you can't get off him except by draining or going through Grendel. The way to handle this is, whenever you do drain (could be before Mayhem, or anytime after such as on Phage), make sure you pick Flash for ball 2, when you'll have a free host change available to get off him.
Assuming you do drain somewhere along the line and then do Flash, then you'll come to Eddie as the last column of the grid. This is where it's worthwhile to avoid finishing the grid - avoid the yellow combo (and the skill shot) so you can do blue and white for the +1 playfield box. This is the time to fill in the other features - the other two Carnage modes, rampage, host hurry-up, bell tower frenzy, and it's also fairly likely to get a second Mayhem here.
Eventually, do finish the grid, then bounce around the hosts to knock off any remaining first-tier bosses, then go for Grendel and Knull. Switching to Gwen is helpful if you can but not critical. At any rate, if you lose to Grendel or Knull, redo the grid with that same host before trying them again.
Galaxy brain move: After finishing the fourth first-tier boss, switch to Gwen, shoot the Doppelganger skill shot, and while Doppel is running you can lock balls and start Mayhem - so do that, pick Hybrid, just aim for the bell tower playfield multipliers, then use Hybrid as you drain out of the multiball. All in order to take Hybrid's big fat playfield multiplier into Grendel!
Galaxy brain move alternative version: If you haven't done a second Mayhem, do this. Finish the first-tier bosses, be on Eddie, start Grendel, but intentionally time it out and lose. Then redo the blue and white combos to regain the +1 playfield box but don't do yellow. Now go for a huge Mayhem with all six locks and Hybrid available!
One other thing to think about: Competition Mode. My Klyntar game was actually with that, trying it out. The big point is that it fixes the Mystery awards: the sequence is always bonus multipliers, 1000 exp, light 3 locks, +1 playfield, start bell tower frenzy. The downside is the mystery will never award any grid box, but that list of awards is all pretty decent and might be worth the tradeoff to avoid the garbage like big points or increase Carnage, and also avoids any problem awards like lighting Carnage too early. (Just know that Captain America's power doesn't work in competition mode, so don't be me and pick him after beating Knull!)