Hey Andy. I got so frustrated I figured I'd try and fix it myself. Here's what I did:
I've worked out a solution that seems to work just fine although I just got it working. Using Windows symbolic links and Google Drive, now called "Backup and Sync" you can save your tool libraries (and I assume your CAM posts, etc) in your Google Drive folder to have available on multiple computers.
This is not a fully tested solution so be careful, make backups, follow at your own risk, etc.
Step 1: Open fusion and make a new tool library in the "Local" folder and name it appropriately. Then open your cloud library and hit ctrl + a to select all your tools, then ctrl + c to copy them. Open your new local library and hit ctrl + v to paste all those tools in. Now you have a duplicate library but stored locally.
Step 2: Make a folder in your cloud folder (Drive folder, Dropbox folder, etc) for your files to live. I named mine "FusionToolLibraries".
Step 3: Go to the folder containing your Fusion libraries located at C:\Users\yourusername\AppData\Roaming\Autodesk\CAM360\libraries\Local and move those .json files to your new cloud sync'd folder, in my case, "FusionToolLibraries".
Step 4: Open a command prompt as an Administrator and make the symbolic links. Symbolic links are basically file shortcuts but as far as programs can tell, they are just the file.
The syntax is "mklink "path to local file" "path to cloud file"
So in my case it was:
mklink "C:\users\Chris\AppData\Roaming\Autodesk\CAM360\libraries\Local\PCNC 1100.json" "C:\Users\Chris\Google Drive\FusionToolLibraries\PCNC 1100.json"
That will make a symbolic link in the Autodesk library folder to the library file saved in the cloud folder. Do this same thing for each .json library you want to have sync'd in the cloud.
Step 5: Do this same procedure on each other computer you want sync'd, but now the .json files are already in the cloud folder so just remove the originals from the Autodesk folder and then make the symbolic links, same as before.
You can now use your sync'd libraries in Fusion by simply using the "Local" libraries instead of the "Cloud" libraries. I don't know if F360 re-checks the files periodically but if you make a change in one library it may not show up in the others until you either restart Fusion or click the little refresh arrows in the top right hand of the navigation pane.
I only just finished setting this up so it may have problems, but so far so good!