As far as i know, there's no way to actually uncook the egg or change it from a boiled egg to a fried one - even the method used in the question about un-boiling only referred to whites. You might be able to alter the texture and perhaps presentation to make your boiled egg look similar to a fried one, if that helps?
Well, solid whites are solid whites - I would expect the texture to be pretty similar from boiled to fried, though you might slice them thinly and fry them if you want the extra grease, hardened edges and browning in your egg whites. Additionally, if you have them sliced thinly, and lay them overlapping on a very hot oiled pan, you might encourage them to stick together (with browned and hardened bits holding the pieces together) in a shape similar to fried egg whites, although it will still be more fragile and prone to breaking at the seams.
Yolk is trickier, since it won't un-set into liquid once it has set up - even the process noted in un-boiling an egg was only for egg whites. A hard boiled egg is dry enough to act as a paste, so just mashing it won't do - on the other hand, adding some liquid (perhaps butter for flavor and color) and blending into a thick liquid could get you a looser, still egg-flavored and buttery-tasty sauce to dip your toast in, very similar to dipping in just yolk. As a bonus, you would likely have more yolk-sauce than you would actual yolk, so you get extra dipping action.
I've used set yolks to make a sauce (although that was gelatinized by drying, not set by boiling), and the result was very thick - it took a lot of liquid and still wanted to set up as a paste when I let it sit. So a set-yolk sauce may turn out to need quite a bit of liquid to reach runny yolk consistency, or it may have a tendency to re-thicken quickly. But I think it would still be possible.