You're going to have this milled, or made from layers? If layers, you don't need to worry about the PCB mounting screws, since you can simply plate mount the switches, and the PCB free-floats off the back, held in place by all the solder joints of the switches. This is how most all plate-mounted keyboards work. So you can make your screw holes to hold the layers together however you like, and be done with it.
If you're having it milled, to use with standoffs for mounting the PCB, we need to know for which PCB you need compatibility. Poker? Also, most 60% PCBs use an onboard controller, so no need to worry about Teensy clearance, since there is no Teensy.
Edit: Missed that you are hand wiring. But that makes it even easier. Your case just needs enough height clearance to leave room for the Teensy. I would recommend M3 screws to fasten all the layers together.