There are many reasons sticking the hdtv up front is a poor design choice.
Will that be an expensive tensioned screen, or will you just suffer a wavy roll up screen, which is what happens
ALL your front speakers are near boundary. It is unlikely they were designed for this. And your center channel is low enough
that the front row might cause issues with hearing dialog.
A large reflective piece of glass on the front wall, where you want absorption?
Why not just put the hdtv out on front, on a rolling stand, that could be stored in the media library room? You could wire in a
some video ports in the front of the stage. And the hdtv would be closer to the seating, not further away.
Or skip the hdtv entirely and buy a cheap second hand projector for gaming use.