So, I received my new power supply on Friday (thus I didn't need to test with any resistor or lightbulb, and besides being safer, I'm sure my test was also more reliable).
No crash so far! (4days and 17h of uptime, which is a new record, I was only able to do 3 days once).
So the culprit was most probably the power unit (I'll keep on monitoring).
Thanks for the help.
The power supply is itself a fairly-complex unit. Stuff goes wrong sometimes (wasn't there something like that in Forrest Gump?). Looks (so far) like you've found the - in the woodpile. Good on ya.