Probably some very involved procedure with duplicating/ consolidating the files from within Avid to a dedicated media drive/ bin, possibly even duplicating the project file externally and loading it as an external bin into another project, all with offlining the bins and media drives somewhere inbetween to enforce the media to be relinked. Either way, this seems like something not even an Avid support specialist might be able to answer off the bat simply because your data management is so messed up.
A wild idea that may or may not help you:
1. What if you exported an AAF (no embedded media) to Premiere.
2. Then exported an XML from Premiere.
3. Edit the XML with a text editor such as TextWrangler or maybe even Dreamweaver to find and replace file paths by using a "Find" seach for /source/mediafolder/ then a "Replace All" command for /destination/mediafolder/. (I think "Find" in both software mentioned is just "command-f")
4. Do the same "Find" then "Replace All" to change file extensions -- .mxf to .mts.
5. Then re-import that XML into Premiere or AE. The only reason I suggest XML's is because they are easy altered in text editors.
****This of course assumes of course your file managment includes the same names for offline and original media.
Also, here's couple things you may or may not be aware in your trouble-shooting process:
1. Premiere won't import AAF's with embedded media, so don't bother.
2. AE sometimes has trouble importing AAF's with audio, so just make sure you toggle off audio on the AVID export side.
Or if you are really lazy, and have lots of storage space, maybe try batch re-transcoding all media on the Avid as Avid 220 (or whatever highest Avid codec is appropriate for your framerate) and then export the worlds largest AAF (with embedded media) to AE (no audio)? Maybe do it sections so its not so crazy.
You are going to be killing your computer trying to work with .mts files anyways. AVC files are heavily compressed and require a ton of processing power to deal with in an edit. You might be better off using another codec for online regardless of how you end up solving this.