You are on the verge of knowing something about shotshells.
There is no big difference in velocity as you have seen for your self.
Choice comes in shot size (turkey 4,5 and#6) and shot material (lead, copper coated lead, or heavy shot).
Turkey hunters take head shots. You want to break the neck or crack the skull.
The further out you want to shoot the smaller the size shot you need.
#5 heavy shot hits like #4 lead but has more pellets.
The larger pellet charges have less pellet count which means sparser patterns.
It is a give and take situation.
If you go with smaller pellets to increase the number of hits on turkey you may only wound the bird.
One pellet that kills is better than ten that wound.
Things to look for would be bore size and choke.
get Screw-in chokes and you can try different contrictions.
Look for an overbored or back-bored barrel.
They should pattern better.
If I was getting a pump I would go 3.5''
If it was auto I would suggest maybe a 3"
Check out
www.wildlifedepartment.com/turkey_loads.htm
Article by Craig Endicot "Turkey Loads"
also goggle "wild turkey zone"