In my experience, painting my own chassis, I found it best to paint the *higher* surfaces first, as the over spray lands on the panel surfaces below. As you spray the lower panels with overspray on them, the fresh spray rewets the "dusted spray" and melts it in. The results would not be so good in reverse.
As I'm sure you've already found, you'll have to turn (roll) the chassis several times to get complete coverage. I sprayed mine while flat, right side down and left side down to get paint into all the nooks and crannies. It's been over twenty-five (>25) years now, but I probably sprayed it "flat" last.
The Healey chassis was my first attempt at using any spray equipment too, so it is indeed a crash course, but you get plenty of opportunity. I still had the sandblast equipment available, and I seem to recall doing a panel or two over again, if I didn't like the result.
My rookie mistake (and a big one...) was partly to blame on running out of time. Because I was going to loose access to the (open air) facility I was using, I applied the clear coat on a foggy January night in Louisiana. The moisture in the air between the spray gun and the chassis surface resulted in a duller finish. The results don't look bad, it may even be more correct for a production car, but I was striving for more gloss. I had to move the chassis out the next morning, regardless of being finished or not.
Then a day later, I was off to do a three (3) week hitch working in the Gulf of Mexico, so the paint had plenty of time to cure while I was gone.