Had my logbook stolen out of my car a few hours after a checkride. I was devastated, but I had photocopied my logbook consistently after being recommended this by an airline HR executive.
Filed a police report to have proof of theft.
Went to the FAA, showed them the police report, showed them my photocopies, they found my 8710 (the checkride application with hours listed), and entered all my totals and signed my logbook. Never had a problem since.
Moral of the story: PHOTOCOPY YOUR LOGBOOK, as the OP writes.
Electronic ones are good, and I use one, but you should copy your logbook to have the endorsements.
I had two sets of photocopies: one at home and another at a friend's house.