As a general statement, unless you use the built-in collection management on the Kindle itself, any other collection management 3rd-party will mean that after you modify the collection memberships, you need to Restart your Kindle (Note, I said RESTART, not RESET, there is a difference!) so that the new .json file with your changes can be read correctly into memory.
So, that said; you could use either Calibre plugin (which I've used, it's ok), or the Kranf one; or I think there are other ones out there as well. I like the simplicity of the Kranf one; you may want to try that one first. You can put the executables right in a subfolder on your Kindle, and run it from the the Kindle. Just read and/or watch the video on how to use it.
http://www.applied-mathematics.net/t...onManager.html
PS: I never thought of using Dropbox as my repository for my Calibre library. I'll have to think if that's a good idea for me or not. Maybe!