Connecting one keyboard to multiple computers simultaneously

So I am working on a project to connect one keyboard to multiple computers simultaneously without a switch.

Need: Each computer will run the same application with the same resolution on the same network.
Problem:
1: The application will not work with traditional remote desktop software so this is ruled out.
2: KVM switch requires switching between computers which defeats the purpose.
Research:
I have searched the internet for a product that can do this using a hardware solution and have come up empty.
Background:
I am by no means am a keyboard engineer. I have over the years open many keyboards to clean them out. I have found that they are pretty simple to design a circuit board with a very thin connection to a membrane which is water resistant and the keys sitting on a plastic housing and some light emitting diodes (LEDs). A USB male cable which extends from the circuit board to the host device.

Solution: Create a double keyboard.

Hypothesis: Two keyboard circuit boards can sit on top of each other.

Steps to prove that this will work.

1. Strip down two identical keyboards.
2. Using one keyboard shell stack two keyboards control circuit boards on top of each other.
3. Make room for two USB cable to come from the keyboard by cutting a notch out for access.
4. Reassemble and then test.
 
Can I ask what is the sense of such keyboard when you can use separate ones for each computer?
 
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