Hopefully others who use MIDI and the like will give you a more detailed answer.
But I will try to give at least $.02 worth of information.
USB on Teensy 4 - LUFA? First off, hopefully a short term issue, is currently the only USB support on the Teensy 4 is for USB Serial, again this hopefully will be a short term limitation. I have only ever used LUFA on an AVR based Arduino, something like an Teensy 2, or in my case another Atmega32U2 board.
So if you are doing a new MIDI device, I would start off looking at:
https://www.pjrc.com/teensy/td_midi.html
As for which setup to use to get enough Analog inputs? For me hard to say. I have never needed that many analog inputs. I believe either of them should work with 3.3v signals. However the Teensy 4 is NOT 5v tolerant, so would need to make sure that none of the signals coming to it were 5v. Now if you are building your own device, that probably would not be an issue as you can hopefully feed all of your inputs with 3.3v... At least for things like sliders and knobs... But again don't know your setup...
If it were me starting off, I would probably experiment first with the Teensy 3.5 or 3.6, to get me going as there is currently more support for them especially on the USB side... If I wanted to try this out quickly and get full usage of all of the pins of either of these two boards, I would probably get one of the breakout boards from TallDog(loglow):
https://www.tindie.com/products/logl...sion-a-dip-64/ (He has a few different versions there) and you can get them pre-assembled. Out of the box you have something like 24 analog inputs. If I needed more I would try bread boarding it up with either of the other Mux boards you mentioned. Since I don't have either I would probably start with one or more Sparkfun ones...
But with this setup, you should hopefully simply setup the Teensy to be a MIDI device and you can start experimenting with your desired inputs and outputs... And then if you find you still need or want more horsepower you can hopefully migrate to the T4, where hopefully by then @Paul will have added the MIDI, and several other USB types like Joystick, Mouse, HID ... support to Teensyduino for the T4.
Again sorry I know that is not much specific help, but hopefully someone else will fill in the holes.