I like tp4's and fohat's ideas expressed here.
Designing a a keyboard from scratch and getting it to work is quite an undertaking.
You (or a close accomplis or 2) will need a wide set of skills in order to pull this off.
Quite possible it will take more than 1 attempt.
Skills needed, offhand, includes:
PCB design
Keyboard theory (n-key rollover, polling,...)
Programming, perhaps in C for any "unusual" features you may have
Soldering (fairly easily learned, just seems scary to some)
Case design and construction
Lots of stuff to learn... Most/All of it, I believe doable. (For me I'd worry about the PCB design the most, but then I'm inherently a software guy.) I think all these aspects are cool and worth learning as a hobby, though I prefer to tackle then one at a time. That way I have something to show or my work and learning curve as I progress.
I'm really starting to like fohat's solution... If I may expand...
Get yourself a small keyboard, maybe 40 keys, programable. Plug it into a free USB port. Place it above your Function keys. Program it. (more keys than you'll ever need!) Success!
Maybe take a look at this (Plank, 47 keys):
https://olkb.com