As a pianist of several years, I don't tend to think that chording is a very good idea for fast typing. Certain chord combinations are never very graceful and are a good recipe for tendon strain. We learn to avoid certain fingering because of these hand limitations, and part of the reason we can do that easily is because we are generally moving our hands all over the keyboard. The secret to effective piano playing (to limit strain and tiredness and harm) is honestly the complete opposite of what a lot of computer-keyboard-minimalists seem to be striving for - pianists are supposed to minimize finger movement, and send as much of that movement upstream as possible. Transfer finger to hand, hand to wrist, wrist to arm, arm to body - limit individual finger activity as much as possible for relaxed playing. The idea of minimizing computer keyboard keys for having less keys, and putting more responsibility on agile fingers while freezing the hand in one location, seems exactly backward if the goal is for fast, efficient, fluid strain-free typing.

1023, unless you want it to spew characters when you aren't touching it.

Realistically one would not want to use the combinations requiring many fingers (the variants using nine fingers gives you just ten combinations more).

Using max four fingers per input still gives you 10+10x9/2+10x9x8/6+10x9x8x7/24=385 combinations.

That already exists. The most popular modern variant is plover[1]. However, it might be hard to transition to.

[1] http://plover.stenoknight.com/

Chording keyboards are mentioned in the first sentence of the post.