It sounds like the problem is due to an underlying maximum path issue with either Windows 10 or Adobe AIR (the platform on which JuiceboxBuilder runs).
Either way, I think there is little that can be done (other than moving the images to a more shallow directory structure before feeding them to JuiceboxBuilder). I'm fairly certain that JuiceboxBuilder is not imposing a maximum path length itself.
Your testing sounds fairly conclusive: fails with a long path; works with a short path.
I've tried to replicate the problem myself but, strangely enough, have not been able to.
I created a directory structure as long as Windows 10 will allow (using the alphabet as a folder name and topping things off with a couple of digital at the end to max it out).
C:\abcdefghijklmnopqrstuvwxyz\abcdefghijklmnopqrstuvwxyz\abcdefghijklmnopqrstuvwxyz\abcdefghijklmnopqrstuvwxyz\abcdefghijklmnopqrstuvwxyz\abcdefghijklmnopqrstuvwxyz\abcdefghijklmnopqrstuvwxyz\abcdefghijklmnopqrstuvwxyz\abcdefghijklmnopqrstuvwxyz01
I then copied a few images to the 'abcdefghijklmnopqrstuvwxyz01' folder, added them to JuiceboxBuilder from this location and the application created the gallery successfully.
Even setting the Gallery Folder on the 'Publish' tab to be the long path above, I cannot get JuiceboxBuilder to crash (under Windows 10 Pro v1703 x64) even though it fails to create all the gallery files in the 'abcdefghijklmnopqrstuvwxyz01' folder.
I think the resolution to this problem is just to use shorter paths.
However, you might like to try removing the default maximum path length that Windows 10 imposes to see if this makes a difference.
It involves either modifying the registry or making a change in the group policy editor. Please see this web page for details.
Please note that I am not recommending that you do this. It is just a suggestion if you are comfortable making changes to your Windows 10 system via the registry or group policy.
Please note that if you choose to make any changes via the registry or group policy, you do so at your own risk.
I recommend that you just shorten your paths before using JuiceboxBuilder.
Incidentally, I have not made this change to my own PC. My tests above were carried out using the default Windows 10 maximum path length.
Also, I realise that the path you posted above is less than Window's default maximum path length of 260 characters but removing this limit might be worth a shot if you feel you want to try something.