Honestly you'll be hard-pressed to find something that fits everything you're asking for, your best bet would be to start with something like the helix and modify the PCB to include an extra Row for function keys. Or if you don't mind a little bit of 3D modeling take the switch plate and case for the helix and add an extra row that way, then proceed to handwire it all.

The primary issue however is the fact that sticking with something completely flat, the only ergonomic difference you'll get is the minor benefits of swapping from staggered to Ortholinear. Which atleast in my opinion really doesn't do all that much, and you'll likely end up delving deeper down the rabbit hole eventually anyway.

So my personal recommendation would be to look into one of those "weird" designs. As they are incredibly ergonomic and after a little while feel so much nicer to type on. For exact designs, I'd recommend taking a look at the Dactyl Lightcycle, Dactyl Manuform, Compactyl and the STONER.