Followup:

57.0.4 has the same problem

56.0 has the same problem

55.0 works, stops working on update

ESR works fine.

I guess I'm stuck with ESR for now, which is a huge bummer.

Did you ever manage to get a Firefox Quantum / 57 or higher version running on your system at all?

If Firefox only worked previous to Quantum / 57, it may be worth checking the microcode (/BIOS) of your CPU to see if an update is available, as suggested in these support articles:

Crash on Broadwell-U with old microcode
Updating processor microcode

In other cases, please see if you can submit a recent crash report generated by Firefox that may be useful. See the Mozilla Crash Reporter article for info.

I believe Quantum was working at some point before it started crashing. My registry reports that my CPU is "Family 6, Model 78, Stepping 3" so if it is a microcode bug, it's not the same one as mentioned in that article.

(also Firefox 56 crashes too)

Right now I've just been running Firefox ESR, since I haven't come up with any more ideas on how to fix it. Here are the two most recent crash reports I have from Firefox:

https://crash-stats.mozilla.com/report/index/1a4da798-540d-4b9f-a911-61cbf0180228

https://crash-stats.mozilla.com/report/index/92cbe6e6-2638-4cbe-bbc5-333b40180228

I think these predate the actual startup-crashes by quite a lot, but they are the most recent ones I have, since the crashes on startup just aren't generating crash reports.

The reports seem to be created in January all right so they may not reflect the current issue.

You could try a clean install and/or uninstall any (recently added or modified?) software as described in the Firefox keeps crashing at startup support article in case you have not done so yet.

Could you also check to see if this question if of help?