Changing from #7 shot to #9 shot will increase the number of pellets in a given weight load by about 200%. Thus if your gun threw a 50% pattern using #9 to get the same density with #7 it'd have to throw Every single one of those little round "BB's" in that 30" circle. You really think it'll do it my friend. Yes going to a smaller size shot increases pattern density even if it has a slightly lower percentage, but that is not an automatic given.
I do not live in prime woodcock country but some years back after a TVA lake was impounded a shift in their flight patterns gave me a few seasons of some shooting. The vast majority of what I killed, along with some wild Bobwhites were taken with a 12ga J P Clabrough having 28" Ľ choked (.010") damascus barrels (Both barrels the same). Load was 1 oz #8's @ about 1150 fps. Shooting was short range, never felt handicapped by being "Over Choked" in any way. I ate them all, none were mangled but they were killed cleanly. The same gun & same load but shot size shifted to #6 was a most excellent cottontail combination when hunting the brush & Briars with a pack of Beagles.
As I said before when folks go to hollering up the advantages of Cylinder bore they virtually always compare it to a full choke.
My personal belief is that modern wads have not really reduced the spread of the pattern to any great extent. What they have done is to eliminate a lot of flyers & put them in the pattern, thus giving that slight increase in density. Haven't done enough pattern counting to be certain, but likely 5% would be more realistic than a 10% increase.
Whether they actually achieved it or not I simply do not know but Lefever advertised 85% patterns with their "Taper Bored" full chokes. Several of their guns which I own & "Presume" to have been bored full choke have only about .030"-.032" constriction. That's about what modern standards are using modern shells.
I said it before & will say it again, A Slight Choke is generally better & far more versatile than either a Full Choke or No Choke.


Miller/TN
I Didn't Say Everything I Said, Yogi Berra