Just a thought, and feel free to shoot me down.
But as pointed out leaving a copy everywhere isn't very practical...so why wouldn't (This is taking a commercial organisation) you leave the original back at Base where its secure and people can't find out what it says but is accessible by CASA or the ATSB in the event its required?
Lets say something becomes defective en-route and you needed that noted on the MR, well call back to the office and let them know, chances are you're going to have to call them anyway to get it fixed.
Leaving the original back at base once its been signed off in the morning and then amending it if required seems to make a lot more sense!!