I have the same set up as you.
My FTMM file goes to the default Family Tree Maker folder in documents, as do the autobackups. At the end of a session on a particular machine I then copy everything across to the Dropbox folder and then when I switch on the other machine do the reverse.
I am not comfortable with storing a file on which I am working in the DB folder, whether it causes crashes or not. Whilst this may have caused crashes, there is regardless a memory management problem with the program.