When we could use lead in CA, I used to use # 2 lead. It worked well with a full choke. You have less shot to make your pattern than # 5's so you're going to want to pattern
your shotgun at different distances to see how well it does. I was able to get solid kills at distances up to 40+ yards but it was aiming my shotgun very precisely at the head (not the neck) and I was using 3.5" shells. CA prohibited lead so I had to switch to steel which sucked in my gun with my choke. I then switched to bismuth with Hevi Shot and my gun is back on track. I'm working through different chokes now to improve my shotgun pattern and am getting tempted to try tungsten loads. But I digress.
The point is you should try # 2's in your gun and then compare them against 5's or even 6's. If you don't like your pattern, research after market chokes for your gun and see how well they pattern. It's more work and more cost but we owe it to game as hunters and it's a lot more satisfying to know you have
your gun dialed in. I say your gun because what does best in your gun could be totally different that what does best in my gun. There are a ton of reviews and posts on the net about just about every single shotgun model out there.
After you finish patterning with different shot sizes & chokes, you will figure out what works best in your gun and what your distance limitations are. Not every gun/choke/shot size combo is a turkey killer past 40 yards. Many are not. But you will figure out how to get the most performance from your gun which is very satisfying. Best of luck and let us know how it works out. I don't think we have a turkey shotgun patterning topic that functions as a tutorial for other members and guests so perhaps you will be able to accomplish that with your posts.