Hi Christiaan,
My apologies, it seems that this post was overlooked!
I’ll try to explain the steps here that we generally take to update the firmware on a SARA-N2xx (on a NB-IoT shield).
Like you mentioned, using a USB-to-Serial converter is the way to go. We’ve tried using a serial pass-through sketch, but it seems this only works with some firmware-versions and only with a 32-bits microcontroller. Instead of using separate wires to all the necessary pins of the shield, you can plug the shield into an Arduino and connect the RX, TX and the GND of the USB-to-Serial converter to the top of the shield (RX=D0, TX=D1).
The sketch on the Arduino should do the following:
pinMode(7, OUTPUT);
digitalWrite(7, HIGH);
pinMode(0, INPUT);
pinMode(1, INPUT);
I’m setting pin 0 and 1 (serial connected to SARA-N2xx) to input, so that we’re sure it will not conflict with the serial converter. This way you should be able to start the firmware uploading process. As you also mentioned, when it requests a reset, the best way is to use a jumper wire to connect the GND to the reset-pad (TP2):

After this it should start uploading the binaries to the module. It is also important to note that for uploading B656 you need CodeLoader v2.14.0.30687 (while B655SP2 needs v2.14.0.31779).
Also, with the information above, I’m assuming you have all the necessary files from ublox (codeloader installations, firmware, UART codeloader manual, etc.). I’m unsure if we can provides these directly to our customers.
Hopefully this helps you a bit. If you still have questions, please let us know!