Well I would have though that the source computer might scan the file being accessed, though I don't know this for certain (I don't have a network to test it) and then it would be scanned on the destination system as that would be a creation of a new file (auto scan by standard shield, depending on the file type).
Have you made any changes to the avast settings ?
You don't mention what sensitivity you have set on the Standard Shield, Normal is the default, if set to high that would increase the number of files scanned.
If this were truly halving cutting and copying performance in half, I would expect to see many, many topics on this, but I just don't see it in the forums and you could say I'm fairly active in the forums. This may possible be why there has been a lack of a response as people aren't experiencing the same problem as you.
What other seciruty software do you have installed, firewall, anti-spyware, etc. ?