I would force it to act like a mouse as part of an expandable system for my project.

Each Teensy-LC pictured below would use its built in USB HID mouse function, receiving mouse moves and commands from a Teensy 3.1 and USB Host.

I can't believe how perfect the timing is for this. I recently received a Circuits@Home USB Host Shield Mini as a gift, and already had it rigged together with my Teensy 3.1. The combination translates the USB data to serial and routs it to the right port.

I could make a 3D printable case file that would include several sizes depending on how many ports you wanted to build, or maybe a snap together system that adds ports to the bus as needed.

Here is the part I really like:

I really do not want to trick the host computers with a hack, as I mentioned in my previous log. This is the part I really want:

Using a separate Teensy-LC for each computer will maintain a continuous connection, allowing for fast switching from the device and eliminating the need for python scripts.

Data Flow:
USB Mouse to
USB Host Shield to
Teensy 3.1 using SPI4Teens3 in the USB Host Shield Library, to
I2C (may change this, but there is a new i2c_t3 library made for Teensy3!)
To each Teensy-LC then output as USB HID mouse moves
Relayed to the right computer.

I Soldered back pins on Teensy 3.1 and pins on the host shield.

Temporally hacked together for testing. Sorry there are not more pictures :( I was going to start a different project for this, but the timing is so perfect to switch to this now.

Some pics that helped me with setup. I used a 100uF cap, cut the VBUS power trace on the USB Host Shield, and added a USB Hub with a 5V power supply.

I promise to get this more organized, with details, pictures and links, that will explain exactly how to get the USB Host Shield working.