I think what you ended up doing is the right thing.
The only way I've found to work in tackling these "just one more thing" users is to tell them this is not accepted behavior here and that they should open a new question with their new problem.
Another thing. When I see these scenarios I usually leave a comment explaining the issue.
Hi, generally follow up questions are usually frowned upon here. If this answer solved your problem and answered your question please consider accepting it. If you have other questions please consider asking them in a new thread instead of adding 'follow up' questions here. Not only are such follow up questions frustrating for the answer giver, they also make it impossible to others with the same problem solve their issue...
I usually try to edit that into something that's more case-specific. I always try to stay positive and friendly towards the OP. It's especially useful when it's not my answer - I think that affirms that it's considered bad by the community rather than the specific user who gave the answer.
Edit: I just left one such comment on your answer. I hope it helps :)
Edit2: Looks like you got your happy ending, I hope this is some indication that this method is useful - at least to an extent.