I've soldered all the diodes, so missing diodes is not my issue. (Assuming that you don't mean LED diodes, which is the part I don't have at all and I currently don't plan adding them.) The only thing that is not soldered are switches. But shorting corresponding PCB points should emulate pressing the missing mechanical switch, there should be no electrical difference between regular switch and this emulation. Note that this switch emulation has worked on the right half.
I also have soldered the capacitor and shorted the two points, as mentioned at
https://keyboard-configurator.massdrop.com/ext/ergodox/assembly as an optional step .
I've also re-checked that there are no resistors to be soldered on the left side.
I've also verified that two IOX pins (12+13? – not sure about the numbering) are not only connected to the Teensy (D0+D1), but they are also connected so some pins of the AVR μcontroller.
I've found program hid_listen that allows me to see the debug output, which has told me more. (I've added several printlns in order to know more.)
I've found some details on blinking: According to the source code and its debug output, it should blink on start and on I2C success. Well, it does not blink on start if TRRS is not connected, because matrix_init»init_mcp23018»i2c_start blocks (probably in while(!(TWCR & (1<<TWINT)))

, so matrix_init»ergodox_blink_all_leds is never reached. Second, it should also blink on successful I2C connection. The successful connection never happens, even with the right end-to-end wiring.
It seems that D0+D1 pins are OK: The μcontroller can detect they are shorted. (When no TRRS cable is connected, they are shorted.) Well, they are at least partially OK, as this means that one of them is able to work as output and the other is able to work as input. It does not tell us whether they are able to do both operations.
Should I post some photos? I've tried to take some photo, but I was unable to get it sharp, so it will require more effort (or a different camera).