I had exactly the same issue, my only solution was mendeley as a one-stop-product. Meaning, I am putting in all my references including the pdfs and use a shared folder. With this you are already having just ONE version of everything. You are avoiding with this solution the problems you already mentioned, but also the citation key issue. Imagining that two people are referring to different documents using the same citation key. What a mess...
So again what I did is the following and this is my solution with overleaf as my central writing tool:
- Using Mendeley Group Folder Function (free for up to 3 users and a total of 100 MB space, very neat if you want to share the PDF files)
- I explicitly synchronize the *.bib file to a shared gdrive folder (dropbox works fine as well)
- I link this particular file with Overleaf via the feature "Upload from URL" using https://sites.google.com/site/gdocs2direct/
- Now I put in a new reference in Mendeley, press sync, file is saved on gdrive, refresh in overleaf. DONE
Why I am not using the direct import possibility of Mendeley and Overleaf? Simply because in that scenario Overleaf is importing from the Mendeley web interface. Unfortunately, Mendeley is not providing in that case certain information such as when the sources was access (for instance URLs).
I hope this answers your question, but I am afraid, if you try to find a middle ground in converting each file of each of your group member to fit a certain style, you will not finish your work in 2030...However, let me know if you find a nice solution :)