That's a really good question.
I have heard that there is a way to "prioritize" tickets on
MDE in case you have multiple tickets linked to a single account. But, I have never figured out how to do it. I was also in a situation where someone in my party had two tickets linked, but as it turned out I didn't really care which one was used which day.
One option might be to enter Epcot using a plastic ticket rather than your MB. That should work, assuming that you get a plastic ticket. Then once that one is used up, the only one left on the MB will be your old NE one. The other option would be to demand to speak with a IT person (one of the people hanging around the entrance gates with iPads) before you go through the entrance to make sure the correct ticket is being used.
Good luck! The worst-case scenario is that you'll just have to spend $5 extra for the MK-eligible ticket when you don't need it (and go through some hassle).
(In fact, after typing that last sentence, I realized that you might as well just pay the extra $5 now, and then avoid any possible hassle that you might encounter. Seems worth it to me.)