Fun idea!
Idea for an extension: You're also playing a game of Tetris at the same time, and you have to choose which pieces go to you, while also supplying pieces to others. Could make for some interesting tension...
Also it would be great to have keyboard shortcuts for selecting and assigning the blocks. E.g. blocks have letters, and places to put them have numbers. Q1, P2, S3. Primarily because I prefer doing things via the keyboard rather than the mouse :)
Finally a shameless plug (thanks to auto-linking) for my own Tetris spin-off: