Yes, the DT in a short race is really a killer as you're pretty much guaranteed not to win at that point. As for adding in a required pit stop on top of a DT, that might be a bit too much, even during an hour long event. Then again it might not make a difference since all cars would have to do the pit stop.
As for when the DT should happen, that would be dependant on if you impose a restriction on when the DT needs to be served. If you allow the driver to serve the DT whenever they want before the last lap, then I think it could be handed out at any time. If you make them serve it within say 3 laps of receiving the DT then you'd want it a bit earlier to allow them the opportunity to make up that lost time by having more laps available.
As you pointed out, a good grid position is essential with this start. A randomized grid can be very handy in helping to even out the field for the first few laps, but then if the DT is early again like it was during testing then the advantage would go to the fast driver that had a crappy grid spot and was stuck behind traffic for the first 1/3 of the race. I'd say do a qual and let the faster guys have fun trying to wreck themselves and screw up intentionally to keep from getting the DT.