In the view of an OPS-inspector, without undue delay might mean before he leaves/releases the aircraft
Nope. If things have to be carried, it says so. If the regulator intended the logbook to be carried, they could have written so in the regulations. Instead they wrote "without undue delay", which is unspecific, but certainly cannot be interpreted in a way that carrying it is the only way to meet that requirement.
I have also kept an electronic logbook for ages. Simple Excel. The UK CAA wants me to self-certify and sign every page of my print-out as true and correct, but has accepted it for everything so far.