Practice all of this before the actual race.
When you initially go to Time Race screen, check box all 4 races at once.
Here are the Chip Start settings I'd use in your shoes.

Auto Finish Gap means that the readers won't indicate any participant's finish time until after the number of minutes that you put into the box: 12
I chose 12 because it's the 5K world record and because with it being a 1 lap course, that seems like a safe number to tell the reader not to track any finish times before 12 minutes into those races.
Once your in the Time Race screen, you'll see all 4 races in the top left with their respective checkboxes right next to them. You can click "Start Listening" anytime before your races so that the readers will automatically start recording official chip start times when you hit the Spacebar to start races.
Obviously you'll checkbox the Ultra and start it at 7AM.
Then you'll checkbox and start the Half at 7:15AM.
Before you start the 6.6K and 5K respectively double check and verify that you have the proper Chip Start settings (above). Then checkbox and start those races respectively at 7:20AM and 7:30AM.
I've done these kinds of races before and they're tough because it's sort of a free for all. What I didn't like about my event was that a lot of people loitered around the finish line which can lead to some confusion when there are different start times and you're tracking chip start times.
#1 you have to triple remind the participants that they must run in the race they signed up for. They can't just arbitrarily switch races and not inform you or the race management/registration staff. It's rare, but you'd be surprised at how much this actually happens. But, as long as participants run in the race they signed up for (and don't switch races last minute without telling anyone), ART does a great job of managing the timing/chip starts for each respective race amongst the free for all and potential confusion.
#2 my race was a lap race (unlike yours), but I still think it's wise to remind participants not to unnecessarily hang out at the finish line to avoid confusion and congestion. For instance, what if you start the 5K at 7:30 AM -- but then a 5K participant shows up at 8:00AM and drops off his gear bag near the finish line area.. then he leaves to go to the bathroom and warm up but is picked up as chip start, and then comes back 15-20 minutes later to officially start the race?? confusing stuff like that happens all of the time at these kinds of races
The ART software handles this very easily as long as you have reasonable control of the congestion that naturally builds at the finish line.