I have spent some considerable time investigating your suggestions. The results are indicated in CAPS below.
1) Create a new .ftm file with one person in it in the D Dropbox folder.
2) Add a media item to that person.
Does that create a media folder as a companion in the D dropbox folder?
If it does, you might consider leaving your current setup alone, just in case - and:
1) Make a copy of your .ftm file with a slightly different name with Windows Explorer and copy it to your Dropbox folder
2) Make a copy of your Media folder with that same name in the format "name Media" with Windows Eplorer and place it in the D Dropbox folder.
Now open this new file in the Dropbox folder and open some media item to see if opens a media item. Add a media item to it and see if it adds it to the Media folder in the Dropbox.
ALL WORKS WELL. I did find that all media items had to be re-linked/re-copied but this was very automatic and quick using the Find Missing Media dialogue.
I go through this same exercise with each version of FTM where I change the year in my file name (ie from 2012 to 2013 in a new folder). That way I always know which FTM program last used that file. I have FTM2011, FTM2010 etc folders with files and media folders in them for each FTM version.
THIS IS SIMILAR to what I have been doing where I have been trying to keep a progressive record every few months of my FTM files by naming them FTM 4500, FTM 5000, etc to indicate the number of people in my file. This where my media folder problems may have started because from recollection I was either renaming or copying the previous version without taking account of the media folder.
Many thanks for your help.