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For a lot of the ideas present here, I'd really suggest looking into Star Wars Legion. It's a system that at its core is very rooted in 40k's core engine geared towards alternating activations. It's also got a suppression system that does a very nice job reducing the efficacy of focus fire. It's got its own problems, but there's some solid ideas to glean from it.

Personally, my solution to injecting alternating activations into 40k would revolve around alternating detachment activations. Likely do something to require multiple detachments (like detachments max out at 800 pts). I think you could go farther with the system, but that's where I'd start.

Of course, the question eventually shifts to just asking if all you're doing is trying to reinvent the new Apocalypse.

If you want to do alternating activations the first thing you have to do is aggressively cut the turn down. Four 'phases' with sub-phases and reactions in some phases leading to units potentially doing eight things a turn (move, cast power, shoot, charge, fight, deny power, overwatch, fight again) just means you're going to need to spend so much time passing priority and figuring out order of activations that the game is never going to finish; most real alternating-activation games (Bolt Action, Legion, Xwing, Crisis Protocol, etc.) let units do about two things a turn.

@Bharring
That's pretty much it. Image guardsmen getting shot at by Intercessors. 5 intercessors won't suppress them, but they might pin them. If the unit buckles down; they won't advance as well next turn but will be harder to kill if they get shot at again. Now 10 intercessors might suppress them (or pin them if they weren't already pinned), especially if they were just shot at by 5 other intercessors. Now the guardsmen scramble to avoid fire; they won't return fire very well next turn, even if they are getting charged.

@LunarSol and @AnomanderRake
I think SomeBloke is going for the Legion approach. I've stated my objections to it; it mixes the personal feelings of soldiers (whether or not they flee) with instinctual responses. Still, I don't think Legion is the best inspiration because it doesn't have as many units as 40k, same with other games. Alternating detachment activations is interesting, I just wonder how Assassins and summoned units will fit in.

The problem with restricting the things a unit can do per turn is that it will encourage taking units with a very high degree of specialization. Why take librarians when you have to pick between movement, melee combat, and psychic powers? You only get 2/3rd of what you pay for each turn and might never use that fancy force sword.