Before we start, I have to emphasize something. The only thing that is changed is a lack of randomness. All sustained damage is exactly the same. That is the key point of this. Regardless of champion, item, rune or mastery (with just 3 exceptions), this would be the exact same dps. So, for AD carries for example, there would be no significant change.
Very little has to be rebalanced. Every crit rune would give you the exact same dps. Every crit item would give you the same DPS. Most every crit champion would have the same DPS.
Abilities that can crit would be easy to fix. Give them the same % damage increase that we would give for champion autoattacks. Statik Shiv can be rebalanced to get the crit% damage increase instead of being able to crit for higher damage, and it would have the same predicted damage over multiple procs, so that's an easy fix. The same thing can be done for crittable abilites like GP Q or Yasuo Q. It's the same dps. The only thing that could be a possible nerf is the crit-fishing gameplay, but that's a pretty small part of most GP gameplay anyway.
The only things that would need to be changed significantly are those who get effects on critting. For example, Trynd gets more Fury when he crits than when he doesn't, so he'd need a change because the actual act of critting is gone. The only item I can think of that has a problem is Lightbringer, because it gives a dot on the act of crit. The only mastery that would need a fix is the one that gives you attack speed when a crit procs. These three things are the only things I can think of that would need specific changes.
Seriously, give me any example of a champion and/or item, and I can explain why they'd have the same DPS before the change as after.
This would take one patch. Trynd, Lightbringer and the one mastery are the only things that would need major changes.
in the mean time an entire class of champions would be in a god awful state of limbo between overpowered and gutted.
I need more info here. What class are you referring to? Why do you think a change that would not affect their dps in any way would affect them so severely? Can you show me some math justifying that opinion?
If I can make a request, I'd like you to explain what you think will take a long time to balance. If you give me a specific example that isn't Trynd, Lightbringer or that one mastery, I can show you math proving that their damage won't be changed. Just give me something specific, and I can prove mathematically I'm right (I'd like to think I've done this already with the earlier math, but I'm perfectly willing to do this again with something more specific as further proof).