I think Adobe's preferred method for transferring work between projects is importing the old project into your new project. If you just want one specific part of the old project, choose to import selected sequences instead of the entire project, and highlight only what you want. Once you get the sequence you're after imported into your new project, you will be able to copy and paste as much as you want. It's possible that copying and pasting from one project to another broke Premiere's link to your original media or some of the metadata for that media.
There have been reports of issues with Copied/Pasted Audio for many versions now. Sometimes, that process works perfectly, but not always.
When it has not, Match Frame has fixed things for many users, but I think that Zach's workflow should be perfect.
Thanks Zack! That seems to have worked. I wish I didn't have all of this duplicate media in my project but that's what bins are for!