Thank you all for chiming in and giving me some ideas of how to interpret these weird fly-offs of my quarry.
And how to diminish them to a deadly end!
So, from this thread and two parallel threads (GTA and AGW) I'm taking away the following:
(1) Buck fever is definitely a factor — I'm sure it has gotten me to forget one (or more!) of the FoM.*
*Fundamentals of marksmanship — sorry, female shooters

— we've got to find a more inclusive term eventually!
(2) Pigeons are incredible tough animals. Even after a deadly shot they still can go long distances before finally expiring. markT says pigeons "fly dead"!
The following two quotes are worth repeating:
—Airspace (aka Guy):
"When I was growing up a close friend and his father raised racing pigeons. I have seen birds fly in that had holes in their bodies from pass though shots from powder burners.
Multiple wounds from shotgun blast and gaping open wounds from something we never figured out.
They are extremely tough and durable birds."
—JadedC, about Cher Ami, a homing pigeon during WWI with a 194-lives-saving message (from Wikipedia):
"As Cher Ami tried to fly back home, the Germans saw her rising out of the brush and opened fire. After several seconds, she was shot down but managed to take flight again.
She arrived back at her loft at division headquarters 25 miles (40 km) to the rear in just 25 minutes, helping to save the lives of the 194 survivors.
She had been
shot through the breast, blinded in one eye, and had a leg hanging only by a tendon." She lived through it.
(3) Hollow points and wadcutters will produce more damage — and less fly-offs.
Just need to make sure they are precise out to range. And that the winds are pretty calm as their poor BC will make them drift a lot more than domed pellets with their typically high BC.
(4) Some suggested to deliver more energy on target.
Well, yesterday on a pesting run the Skyhawk (30FPE) lost all its air — pffffft. Bummer!
Fortunatley, I had the PP700 (.22) with me, and it killed just as well, at only 11FPE.
Suprised me. (And yes, at longer ranges the 30FPE does deliver with more precision, both through a flatter trajectory, less wind drift, and sufficient power to brake through the feathers).
(5) Pigeon anatomy for shot placement — yes, I think I can improve my shot placement!
For me that means higher and further forward than I used to shoot.
(6) I have all the equipment for exterior ballistics.
But I should
do target practice under the same conditions that I hunt — so no bag under the buttstock, no comfortably sitting in a chair — but standing in a feeding trough, the bipod on a fence post....
Then I'll know what I'm truly capable of hitting....
THANKS again, this has been very helpful to me to think this through with people much more experienced than I!
Matthias