Pattern density, velocity, and pellet penetration are the balancing legs of the triangle.
A fairly well established rule of thumb regarding penetration that has worked out in the field for me, has been the use of strong metal tuna or soup cans to determine the max distance to still get penetration with whatever shot size is being used that will break into the small walnut sized turkey skull or the #2 wooden pencil sized neck vertebrae for a kill.
In your examples...set up a tuna can at 20 yards so you looking at its 3.5" wide bottom...and see if the 7.5s cleanly punch through...if so, move it out another 5 yards, etc...you get the idea.
The balancing act is while the big heavy #4s will penetrate at about twice the distance of the 7.5s, their pattern would be so thin you probably wouldn't hit those tiny vitals.
But if you go with #7.5s to fill the pattern to ensure killing hits every time, their penetration distance shrinks you back back up close.
Surprised to hear about the #6s not working which have always turned out to be my optimal turkey load in 3 different .62cal smoothbores now.
Using the 1:1.5 powder/shot ratio for medium size shot, mine has been:
80grn measure of Goex 3F
Two Oxyoke wonderwads
120grn measure of hard magnum #6s
Circle Fly OS card
Punches right through tuna cans at 40 yards...took one Tom at that distance...others in the 20s and 30s yard ranges.