HOw to criss-cross two keyboards with 2 PCs.

I asked about this a year or two ago.  Now I think I've simplified my
needs, and if there's an answer, it should be simpler. 

I have two computers, a desktop and a laptop with external keyboard (and
mouse). 

The two keyboards sit one above/behind the other and the rear one is
hard to reach and type on. (I've tried voice-to-text and it's good when
it's good but has frequent problems.) 

I'd prefer a hardware solution, I think, but software is good too, so
that I can switch KB-A to work with PC-B and at the same time switch
KB-B to work with PC-A.

  (Normally KB-A will be with PC-A and KB-B will be with PC-B.  I just
want to criss-cross them sometimes. )


My impression is that KVM switches make the keyboard, for example, work
with the PC you choose, but don't do anything to make the PC you'v
demoted work with the keyboard you don't like.   And that I'd need some
complicated arrangement of two KVM swithces to do what I want, unless
someone has already done it.