Interesting approach to use kinematic bodies! That's actually pretty clever way to save some coding time for a jam.
I have no idea what the "normal" way is to code Tetris, but I just used a 2d array of simple struct objects that I just had a few attributes representing each cell on the game board. And then from there is was just a matter of having positions correspond to those cells and basically moving blocks around on them.
I'm sure there's lots of places where my code was needlessly complex, but I think it got the job done.
Also! On the GMTK stream today I found a new competitor! They took it in a totally different direction, but it's still.got the core idea of Tetris blocks building the level for a player.