I have finally started the switch over to using Google GMail as my main mail host and my personal hosting as a backup. I have often had problems copying messages between accounts in Thunderbird (slow, sporadic crashes) and there was no difference with GMail – “cannot append message. (failure)” errors that stopped the whole copy, not just that one message.
So I found (for the second time) that IMAPSize does a very good job. You have to list each folder in the messages pane and then right click to get the copy menu. Then leave it be.