I soldered wires to DTR#, RTS#, GPIO0 and RESET and made the reset circuit from the NodeMCU schematic on a breadboard using BJT's instead of the MOSFET's on my PCB. I managed to successfully program the ESP again, but only once. Now it won't program anymore, and I get the same error as I did before:
warning: espcomm_sync failed
error: espcomm_open failed
error: espcomm_upload_mem failed
Using a logic analyzer I see that the DTR# and RTS# lines don't respond when I try to program the ESP.
Back to debugging again...