let me suggest two things.

1) your going about it backwards meaning plots with check-boxes are show in Help for Manipulate using PopupMenus, but not for PopupMenus with Dynamic. Using Dynamic will be more difficult unless used as seen in Help. I would guess it's possible but "lower level" usage, and so there will be less help and potentially less support with future versions.

2) see: ref/CurrentValue

3) you might consider using ChoiceDialog or some interface element designed to return a choice.