This is what I do as well, only it usually doesn't take more than 2 doors before he's dead anyways.
A lot of people don't seem to understand that you can open 1 of the doors early either, and unless you have multiple people running to open doors (which is bad, because some derp will always fuck it up) you're not going to have time if they're on opposite sides of the room.
If your healer is confident then optimally they should do the doors solo once they're marked. Basically on the grounds that Diabolos is not dishing out damage while he's chargin' his lasers, but you can still DPS him.That's' what I do with my fc members. And we split the task so each of us is looking for his pair. Fastest, safest way to do it imo.
However, I can certainly see the value in splitting the responsibilities of marking the doors initially.
if your DPS and healer are good enough (probably arent by the sounds of things, but still) you can skip opening doors on the first ruinous omen and then open doors for the second; shouldnt be any more after that. that way you only need to worry about a single set. can pre open one of the doors then open the second around 50% or so and you'll be fine.
Definitely want to watch that cast bar, especially if the pair of doors are right beside each other. Too soon, and you emerge right into Ominous. Too late, and, well, you know how that goes.
-Balls