And one other point -- I think it's good to be immediately skeptical of any theory that depends on a faked death.
First, there's the problem that any theory invoking a faked death has to remain forever speculative, unless some evidence surfaces that clearly and unambiguously proves it. That is, there is NO other scenario that will work.
Second, there is a usually a simple logical problem with speculating about a faked death. Here, the problem is that there would have been many people who could have benefited from the king's favor if they had reported the fraud. Yet none of them came forward to receive that bounty?
Third, just personal experience, this is arguably the most common plot device for fakers in general. I know half a dozen guys who are Habsburg princes because some 19th century Austrian prince faked his death and ran off to South America with a mistress he secretly married. Fakers all ;)