Hi!
Great initiative!
I'm also working on a similar solution. Real time pitch shifting. If you are @home in Assembly, the following page might be of interest:
http://elm-chan.org/works/vp/report.htmlASM code if available for download at the bottom of the page...
Also, as an microcontroller, the ATtiny1616 might be a good choice.
It has a DAC, hardware multiplication support and a 20MHz internal oscillator; so no crystal needed and at the time of writing it is actually available ;-).