Our solution
OK, this is what we did for multiple users, it could work for this situation though if you always want the same desktop background for all.
Similar to D200's comment; We created a dedicated folder for Desktop Backgrounds and then put our default background in there.
Then we set everyone's Desktop Background to cycle through that folder. Any time we want to change the default Background, we just change it in the folder and 5 minutes later everyone has it.
You would have to do it once and then you could just change your pic in the folder any time you want.
And I have to agree, if I had to delete a bunch of spaces and reset all my app assignments just to get a unified background, that would be a terrible "solution". What if you change your mind tomorrow and have to do it again?
Why can't they just have an "apply to all spaces"?