I handload 12 gauge but specialty loads only.
I don't shoot much in the way of clay birds anymore so I just buy Walmart 100 packs of #8 shot for that.
Your middle pic looks likce your best pattern, almost as tight as my handloads of #5 and #6 shot shot 1.5 oz loads.
More is NOT always better.
I beat the pants off a guy with a 10 bore magnum shooting 2.5 oz shot.
He was so humiliated he accused me of cheating.
Cheating and what and why and how escapes me.
Like I siad I manufacture NEW ammo by using new, primed hulls, everything else has to be new so I can't call them "reloads".
My #2, #3, and #4 buck pattern ultra tight.
The #2 and #3 buckshot shoot inside 20 inches at 40 yards.
Another reason why I put "ghost ring" adj. sights on that 11-87.
For many reasons I have no use for the marbles like 000 and 00 buck.
Don't use buck for deer but I'd bet a chest full of #2 buck under 40 yards should do in bambi pretty well.
My new manufactured buck might do better on for deer with #1 buck.
I'll have to try that load on paper one day.
My turkey loads are all 1.5 oz. put up in new 3 inch multihulls, sometimes Fiocchi, correctly and well buffered, M.V. is around 1100 f.p.s.
You can drive a load too fast and get poor patterns.
#4 buck will NOT pattern as tight as the #2 and #3 loads, in fact the #4's act like birdshot giving me about 95% at 40.