check mej17's gen 6 megathread for the type based tms script
https://www.pokecommunity.com/threads/314567
at any rate it is possible to display your team and you don't have to bring it up like USUM. the code needed for that would be simple calls
@pokemon.icon, @pokemon.hpmax etc. so you can copy a lot of the code from the summary screen into the section that reveals tms in your bag
you would also have to edit your bag bgs specifically the screen. Since you're using a single screen it may be more efficient to display the icons without their HP bars. You'll also have to have the tm info pop up which can cram the screen unnecessarily. Since pop ups are a thing, you will have to create a new method possibly pbTmCompatiblityScreen and all of the relevant controls to bring the compatibility chart up to make it make sense with the rest of the bag ui (sort like how the screen to select a move to overwrite)
at any rate, here is my idea of using the default bag ui (any other custom bag uis need be variations on this theme):
there are to possible options: a check or x mark OR "comaptible/incompatible" notice how far the icons were pushed becuase even in Power Green Narrow at 8 font I could barely fit them in at the proper resolution!
the check or x icon would be better. It would be a simple overlay or imagepos.push().
It's possible and good luck!