Other than mining (preferably solo) and running bitmonerod, is there anything else that regular Monero users can do in the immediate future to help defend against the expected attack tomorrow, or allow faster repair of the damage if any?
If there is evidence of an attack or even when an attack seems likely the best thing to do is simply not engage in transactions. The old part of the blockchain will be fine regardless.
We don't find credible the claim of an attack against private keys (see mathematical analysis posted here). Of course we could be wrong, but we will cross that bridge if and when we come to it. No one can guarantee zero risk, but we believe this risk is very low.
You don't need to personally back up your blockchain, if there is an kind of attack against it there will be an update that will recover it just as there was with the last attack, which was likely far more sophisticated in terms of technical knowledge required than anything BCX has in mind, but that is just my guess. It can't hurt though.
Don't panic (ever). Wait for further updates.