I think a working solution is achievable ...to be able to explain it in detail would require the solution to be ready to use.
I think the solution will involve some work from the individual - that might be a case of uploading images to a new server and then some work from Martin's HQ side to wave a magic wand and re index the images in the Mayhem database. This would be done using SQL ( Structured Query Language) which is the tool you use to manage data in a database.
So trying to show what I am talking about - picture (excuse the pun) a database containing 100,000,000 records each with the word "there" and you want to change that all to "their" - you would create a script that updates all occurrences of there to their - run the script and all would be changed - the execution time would be a few tens of seconds to achieve this.
So imagine that a photo link stored in the Mayhem database for user "A" is
http://s1143.photobucket.com/user/bobkiralfy/media/K%20Class/hull-join-2_zpsjbkiygdz.jpg.html
and you want it to be
http://newimagestore.co.uk/user/bobkiralfy/media/KClass/hull-join-2.jpg you write the code to get the new URL and use SQL to update the record in the database to allow the post to retrieve the image from the new storage location. This could be run on tens of thousands of database records in seconds, only happens once to change the url for the image in the database.
The involvement of the owner of the images would not require them to understand anything technical that I am talking about - that side of things would be done for you by Martin running a script.
I also think that you may be able to disregard all I am typing as I think it's highly likely that images hosts - especially the one Marin is looking at will come up with an application to get the images out of Photobucket and stored nice and safe somewhere else and then with some clever jiggery pokey with a scripting language on the web server hey presto your images appear.
So I would suggest the future is bright - just that it's a moving target so it's difficult to be certain until some stakes are driven into the ground with a new solution.
Hope that answered your questions - these are my thoughts not Martin's so don't blame him if it doesn't work out.
C-3PO