Very very simple; your making this more complicated than needed, but since it's new for you, that is understood.
Set up your draft as the EXTENDED DRAFT option. Start it immediately, disable the draft robot.
As your picks are made off-line, you then can go in an make the selections for each owner. You'll see the player moved to the owner's roster, you'll see the player removed from the draft pool, etc. And, if everyone has access to the site during the extended draft, they can always go in their on their own when they're on the clock, and make the pick on their own.
As the Commish, you can draft the player for every owner. When your ready to go 'live' with everyone in the draft room at the same time, the room will be there waiting for everyone.
The only trick is I'm not sure if you can set up a time limit in the room, when you get everyone in there. If not, just keep the time yourself during each pick with a stopwatch. That will work.
Once you start the extended draft, you can't turn it pick to a timed draft. But it accomplishes everything you want..