I like it!
Hmm... one hour painting intervals are tricky. I wonder if you can find some kind of quick drying, low-fume spray paint that might work?
Here's the first thing I would try... and, obviously, I would experiment on materials in the garage before trying any of this on the actual brace.... Maybe find some kind of light grey paint that dries inside an hour, do this incrementally:
Day 1: spray on the base gray color.
Day 2: having made custom decals for the stripes, boomerangs, and delta shield earlier, apply them to the brace. Should be good to go after an hour of drying in a warm room.
Day 3: use dry transfer lettering to mark the words. Or cut the letters from a sheet of black decal film. I wouldn't recommend printing them on clear film as a quick drying spray will likely be a flat finish and you'll get a bunch of silvering if you use clear film anywhere. (edit... If future acrylic floor finish dries quick enough, you could coat it with a layer of this and then use clear decals on the glossy surface, then go to step 4 below.)
Day 4: hit the whole thing in some kinda clear finish. I wonder if Future dries inside an hour... I bet it might. Especially if you do a few thin coats; one per day.
Again, test all this on some kinda similar plastic as the brace is made of before you have at the actual medical device.
BTW, What is that thing made of anyway?
P.S. Your son is adorable. I dare say he may well even be cuter than my boy was at that age... and that's saying a lot!