The trackball harness he sells is for a Happ trackball. I'm 99% sure that the connectors and pinout are different so I doubt that it will work.
I think that you need to buy the "USB interface with L/R mouse buttons" for $12.50 and then wire up the connection to the trackball yourself.
You'll need the L/R button support if you plan to use the trackball as a replacement for your windows mouse in your cabinet.
BTW, I have the same issues with the size of the mounting plate. I'm trying desperately to squeeze 2 ultimarc trackballs, 2 tornado spinners, 4 T-Stick Plus joysticks, and 26 buttons on my control panel that's about 37" wide by 14" deep. And that's just the top. The box under the top limits the control area even more.
I've got some interesting ideas on how to install the trackball plates that should gain me a little room but I'm sure it's going to be insanely cramped no matter what I do.
Regardless, MDF is fairly cheap, so I'm considering this a dry run. If I build it and it's unusable, I'll make another with just one trackball and maybe a few less buttons.