If the addons have in-game configuration, see if they have a section for "Profiles" and if so maybe you can switch the new realm characters profile to the old one.
Other wise in the WTF\Account\[your account]\SavedVariables\[addon name].lua file you might find something like
Code:
["profileKeys"]
["CharacterName-RealmName"] = "Profile name",
You should be able to change the RealmName (save a copy or two of the file before changing it).
I also thought TrinketMenu's SavedVariables were per character but it's been a while, ItemTack even longer.