I think you might run into problems with analog measurements, especially with voltage drift caused by changing temperature.
I would go with the 'expander' solution. Use one pin to reset a Johnson counter (CD4017?), another to clock it, that gives you 10 sequenced drive signals to the keys and 4 inputs still unsed to read the keys back so even if you use them as they are, you have 40 keys already. If you use a diode matrix (or better still, a binary encoder IC) to encode the return signals back to four bits you can read 160 (16 x 10) keys back. The advantage of doing it digitally is your software can look for more than one key being pressed. If you do it using analog methods and press more than one key, the resulting voltage will not represent the two notes you pressed but a single other note.
Yes, that is how PC keyboards work, in fact how almost all keyboards and keypads work. In a PC, the keyboard has it's own processor that scans the keys and converts the key number into a code which is sent serially to the motherboard. Similarly, it receives serial commands to turn the indicator LEDs on and off.
Brian.