This is the culmination of my project. I was able to take pictures of most of the steps and the majority of the components so they are arranged relatively chronologically below with comments.
In order to connect the Teensy to my computer, I purchased a short panel mount USB Micro B to B cable and mounted the B end to the pickguard. This way, I can use a standard USB B to USB 3 cable that are readily available (USB B is used on standard home office equipment like printers and scanners) and not have to worry about breaking the Teensy inside with a cable connected directly to it.
Here are the guts of the project. I used a small generic PCB (printed circuit board) and soldered a socket for the Teensy so that I can remove it in the future if I want to use it for other projects. Following my schematic, I laid out the board in a way that would compromise the layout of the Teensy's data pins with the ergonomic layout of my components.
Almost done, except for the buttons again (these arrived later). You will notice there is a 5-pin MIDI connector mounted between two of the guitar's volume knobs. Initially this was going to serve as the audio tether to and from the computer. I made a 4-line cable with a MIDI connector on one end and a 1/4" TS split on the other to send the audio signal to and receive the summed loops from the computer so that the raw guitar signal and the loops could be sent out the normal output jack directly to an amp. Unfortunately, in practice, this introduced quite a bit of noise into the signal and created a feedback loop somewhere in the circuit. I had planned on simply splicing the two signals together at the output jack but this led to the above issues. To do it correctly would have required an analog summing circuit with an op amp which I did not have time to engineer so I decided to rely fully on the computer for audio routing and just send my guitar signal into my interface and take normal outputs from there.
Above is a short video of the controller working alongside my Ableton session.
Above is my Ableton session for this project. From left to right I have an input track from which the raw guitar signal is monitored, 5 loop tracks which get signal from the input track and send to a single aux track to the left of the master track which sums all 5 and can modify the out-going level of all 5 loops together. Finally there is a record track to the right of the loops which takes signal from the master and records the entire performance in an audio file. The looping is done with Ableton's Looper plug-in, each of which is controlled via the MIDI signal from the Teensy.