I've not dealt with what I would call a "rough start" issue on my car, but I know that on my current civic, you want to wait for the CEL to go off before you start the engine cold, but if it's warm enough that the temp. gauge shows anything, you want to crank the starter immediately and not wait for the fuel pump to run - waiting for that, then cranking on a warm or fully up to temp. engine will result in it turning over several times before it starts, whereas starting as soon as you insert the key gives an immediate startup as you'd expect from a warm engine.
I've investigated several things and I'm quite confident the issue is the engine actually getting too much fuel (in the initial "wetting" spray) on warm startup, whether the fault is the ECU(not my guess) or one/some of the components in the fuel system.

You may have already tried this, but if not, do what I've been doing: you can let the pump run like normal (until CEL turns off) before you crank the starter if the engine is cold, but if it's warm or has been driven fairly recently, just turn the key directly to crank w/o waiting. If that doesn't help at all, or it's seems to but it's random, off and on, etc. than it's probably not that it's getting too much fuel during that 2second pre-start spray, but something else (fuel-related or otherwise).