I read that Synergy has security risks because of how it's setup. Do you have any familiarity with that? The computers that I work off of are keylogged/big brothered and can't share data in certain ways.
If any of your machines are on a VPN connection, Synergy won't work. Most Windows corporate VPN configurations prohibit being connected to the VPN and talking to local network endpoints at the same time (to avoid inadvertently bridging your home network and the corporate network).
Plus, it's well suited to machines with monitors next to each other, less so for totally separate machines. And it requires everything to always be powered up.
Is there a reason you need the laptops? My shed office setup has an iMac, plus a few monitors for Windows/Linux machines, though I've got a big "L" desk, and quite a few keyboards. It doesn't really bother me to have... um... *counts* 4 keyboards, 6 monitors... a couple KVM switches... when you throw in some utility Raspberry Pis on the edges, there's quite a bit of hardware in there.
I don't know the details of what you're doing, but if you can't rely on USB-C/Thunderbolt docking, it's going to be a pain to get all that working seamlessly, and I agree with the "KVM switches are a pain" assertion. Plus, the cheap ones don't support high resolution, and the ones that support high resolution are staggeringly expensive. I've got a few systems on a KVM switch, but I bought a super cheap VGA/USB KVM, don't use the VGA, and just manually switch monitors between inputs as needed.