First, the problem with bad patterns usually means your shot column is torquing as it comes down the barrel. This is why rifles don't shoot shot well, and you don't need much of a turn in the shot to cause you problems. Increasing powder only amplifies the effect.
It's a myth that the wad will fly through the shot causing "donuts". I've seen the photos, and in none of them does the wad show itself ahead of the shot. Add to that the fact that the tiny spheres of shot have much less air friction than the wad, so the wad decelerates at an amazing rate compared to the shot..., and you will know it's not possible. Hot gasses blowing around a poorly fitted solid wad, or through some tow or paper used as a wad, is a different matter..., but a wad itself..., nope.
The key is to reduce any of the movement of the shot column. In fact Remington for their modern shotguns markets a turkey choke that not only is very tight... it also is straight grooved to prevent or to halt any twisting of the shot column.
As I mentioned, adding velocity by adding powder won't help your problem. In fact reducing velocity may help, and many folks do this by default for they add more shot by volume than powder. So if you use 1¼ ounce of shot instead of 7/8 ounce without adjusting the powder quantity, you will have more pellets but also lower velocity. If you go too far with the shot amount, you might seriously reduce the effective range of your shotgun.
One method that works for some folks... try 80 grains of powder, followed by a 1/8 cardboard wad. Then using a dipper or measure set to 30 grains of powder..., load some shot. Follow it with another 1/8 wad... then another 30 grain dipper full of shot, followed by another wad, and then a final 30 grain dipper of shot, and a final wad. You will then have shot equivalent to a 90 grain load, spaced out with four wads. This should reduce any twisting effect on the shot column, and gives you a bit more shot over the powder.
See if that helps.
If you find a load that is satisfactory on paper, then do a tuna can test. Get an empty steel tuna can, and set it down range at your desired maximum distance. Set it on its side with the bottom facing you, and take a shot at it. If the pellets don't penetrate, you need to work on upping the power of the load, or..., you need to lower the max range where you will shoot the turkey.
LD