The restoration folder can probably be adjusted to work for the MPC One, all it does is copy the contents of a 'Data' folder to the MPC internal drive. The contents of that folder are two sub folders; 'Demos' (containing project files) and 'Expansions' (containing a sub folder for each included expansion).
Looking at the script, I cannot see anything unique about it other than it copies the folders. The end. No permission setting, no other actions, other than stopping and starting the MPC.
The question is, what is the MPC looking for? What missing data is causing this issue? Is it just needing the folder structure to be there (with no actual data inside), or does it need to discover the specific projects themselves (e.g. the demo XPJ files etc)?
I don't have an MPC One, but my first thought is to try to create the folder structure yourself, with no data, the data itself might be irrelevant.
First you'll need to find out what the missing folder structure is. I assume it's potentially the same as the MPC Live. Can any MPC One users confirm?
The browser doesn't have a 'create folder' option, however there is one in the 'save' project screen, you could perhaps use that 'save' screen to navigate to the root location of the internal drive and hit 'New Folder' and create the folder structure you need. You could even save a project inside a newly created 'demos' folder.
Unfortunately I'm not about to start messing with my MPC Live like this. Personally I would recommend you head over to Facebook and join the
MPC hacking group, they are the ones to talk to about this, they will probably be able to 'adjust' this installer for you. You can also try tagging Dan Gill there (Akai's product developer).
Another guy to try is Andy Mac, he can sometimes put you in direct touch with the correct support person.
https://www.facebook.com/andy.mac.75457But do be courteous and polite with these guys, they are not tech support, they are head of product dev and head of marketing respectively so don't get upset if they don't answer you, but it's worth a try to see if they can help.