Ask HN: How to best deal with 2 computers, but a single control keyboard/mouse

Due to a new contract, I now have to actively manage 2 computers during my day. One for the new contract, and another for my existing open source work which requires me to keep in touch, etc, and I'm having trouble figuring out how to ergonomically handle this.

Currently I use 2 or 3 24" monitors where the center one is directly in front of me, for simple ergonomics. I use one or 2 side monitors for other stuff, chat, youtube video, music or reference material. This has always worked great, as I can have my code on the center monitor where my focus is.

But now I'll be about 1/2 time on one computer, and 1/2 time on the other, but would still like to keep tabs on the other thing. Of course multiple monitors allow this. But what is the best way to have the center monitor contain what I'm trying to focus on at that time.

Right now I'm thinking of how to use a KVM to toggle the input of the center monitor. And then use the wing monitors for email/chat notifications of the different scopes.

I'm used to context switching in my head like this, so I'm not worried about the cognitive load. I've just never been forced to use a dedicated computer for a specific contract. This is more about ergonomics for me.

Thanks.