Teensy++ and centepede shield

That's correct. You can string the shields together with a few wires, connect the SDA and SCL in parallel. I don't have a Teensy to test, so there is no Centipede Library for it...but you should be able to get it working quickly, the library is merely convenient.

A chess board is also the perfect layout for a matrix arrangement...you may not really need that many channels. The reed switches could easily be read with 16 pins.