How dominant is turkey tail?

Short version: Is there any hope of shiitake, lions mane or blue oyster outcompeting turkey tail in maple wood?

This winter we had to cut down 2 old sugar maples. It took a while to get spawn and the spring was very warm but I went ahead and did sawdust spawn inoculation and sealed with wax.
There were signs, on the done longs, that there was some mycelium growth, so I was hopeful. We got some heavy rains last week and when I checked there are the starts of what are clearly turkey tails fruiting bodies all over both the stuff I did and all the logs I didn't do.

I am just wondering if there is any hope for any of what I wanted to grow through? ( I think I have a buyer for the turkey tail, so it's not a total loss but....)

I've had similar problems before. Turkey tail is one of the most common "weeds" of mushroom logs. They will definitely decrease your yield of shiitake, lion's mane and oysters. but there is an excellent chance that you will still get some mushrooms of the desired species- just not as many. In this situation, I remove the turkey tail, dry it and then continue monitoring the logs and keeping them moist. Time will tell. Good luck!