Updating through Cura is for the older 8 bit boards (and maybe some early 32 bit boards) after flashing a bootloader with an Arduino. The SD card method is the de facto method for the E3P. A few questions about your attempts at updating that way:
1. Was your SD card formatted to FAT32?
2. Was the filename unique or just firmware.bin? E3Ps won't flash a firmware with the same filename twice, so if you used a generic enough name it might not work. Marlin compiles with a time/datestamp in the filename for this reason.
3. What happened when you tried to update? Nothing at all? It's pretty hard to tell as the biggest thing that happens is a slower than usual bootup unless you go digging. Other than that, I noticed some slight menu changes and the chinkspeak "Print from TF" now says "Print from media."
Also, trying to level this fucking bed has been a huge migraine, even with a BLTouch. I finally replaced the garbage stock extruder and hotend, plus I picked up another Pi to run Octoprint. When I try mesh levelling I keep getting an M112 or hilariously fucked results.