For the sensing, you could use capacitive sensing, light sensing (e.g. block an IR beam or an LDR installed under the floor) or pressure pads (various types available or make your own with Al Foil)
So for example, you can do this easily with a small microcontroller with a cap sensing peripheral. A PIC16F1519 is an example with 28 cap sense channels (if you need more then there are other larger options) and only costs $1.37 in volume (so proabably ~$1.80 for 1)
You would install sheets of copper/aluminium foil under the keys, and attach to each channel. Tuning the setup probably wouldn't be too hard as you will likely get large changes compared to finger sized solutions.
For the pressure pad version, you can use something like these 1.75" x 1.5" resistive pads and attach directly to an input pin with largish pullup (or use a comparator):
Then you can either use the micro itself to generate the tones (e.g. Filtered PWM) or send a MIDI code for each key to something else (e.g. synthesizer, PC, etc) to play them.