So I've found a workaround which seems to point to an issue with LR talking to a server somewhere.
If I disable my NIC and run LR CC offline, no crashes. I'm able to load and upgrade old catalogues, create new ones, import files, edit images, etc and no crashes whatsoever. Closed LR and enabled my NIC again, ran LR and the same crash happens as before 100% of the time (i.e. I literally cannot use LR at all)
I can see LR trying to contact two sites:
(this is from preferences.wfprefs in AppData\Local\Adobe\Lightroom\Preferences
The solution for most folks is to open their Creative Cloud App, click the gear, click Preferences, Sign Out and then Sign back in.
If that doesn't get it,
As I said in the original post, I logged out and back into CC (multiple times, in fact)
Only thing I haven't done is anything involving SLCache\SLStore. Will do so tomorrow.
However I'll be VERY surprised if that solves anything. Disconnecting from the network and running LR CC offline works absolutely perfectly. This being the case, I can't imagine SLCache\SLStore having anything to do with it.
But will try anyway. You never know.
Well, I've found a workaround that allows me to be online and have Lightroom CC work.
Blocking Lightroom 6's exe in the outbound rules of your firewall (in my case just Windows 8.1's firewall) has fixed the issue for me for the moment.
I'm going to mark this as the correct answer. Hopefully it helps others.
Sorry, when I say "Lightroom 6" I should really be saying "Lightroom CC"
Weird, this is so true! Initially I thought this was a GPU thing, I am running two GTX 980's and Lightroom randomly would crash every few minutes. I blocked all outgoing network connections from Lightroom and now it is stable again. Anyone at Adobe care to enlighten us as to what is going on?