Larry, the main problem I see with using smaller shot, such a 9's is that most of us aren't able to consistently hit our birds with the center of the pattern. I often only hit them with the fringe of the pattern. Using the 7's one pellet is often all that is needed to penetrate to the vitals but a single 9 seldom has enough energy to put a bird down hard but they fly off to die later. Now, all I shoot are wild birds and the action is quick and often unexpected and on very uneven ground with mesquite trees everywhere. So, quick intuitive reactions are critical and no time to plan where to center the bird.
Joe, it's worth noting that "period" literature on shooting woodcock makes reference to using 10's. (John Alden Knight's "Woodcock", for example.) As I've noted above, I tried one box and determined that was enough for me. The good thing about 9's and open chokes is that they tend to fill out a pattern very nicely. Were that not true, skeet shooters wouldn't use them. And having walked around skeet fields and picked up unbroken targets with at least one hole in them--sometimes 2, rarely 3--it's a certainty that good skeet shooters aren't counting on single pellet hits to do the job. But they seem to work quite well on woodcock, which are often shot very close (and also very quick) before they disappear in the cover. Outdoor writer Steve Smith, who's shot a lot of woodcock and lives in northern Michigan where he doesn't need to travel much to find them, once paced off woodcock kills and recorded distances: Average of 13 yards for first shot kills; 15-16 for 2nd shot kills. They're not particularly fast, but they often don't need to fly far to be out of sight. That, I think, explains very open chokes and 9's. Maybe something larger in the tighter choked 2nd barrel.
I'm sure you have a bunch more experience on bobwhites than I do. I'd never use 9's on them. 8's seem to be a better choice, or even 7 1/2's. Especially the latter for a 2nd shot, because they're a lot faster than doodles. And most of the places I've hunted them, at least sometimes they stay in the open long enough that you can take longer shots than you're likely to get very often on woodcock.