The Doctors program is "transferred" - cut and pasted - into various places throughout the series, and never copy and pasted. This is, IMO, a mistaken approach, but at least it is consistent. It would suggest that copy an pasting the Doctor would not work, or it would have been done in many situations.

I understand that his memories would not be consistent if he made copies, but they certainly do some re-modelling of his memory on occasions. And I am not sure why missing a few momories is such an issue - one version would have some memories, isn't that enough?