Because I am an anal-retentive friend of the Pegasus committee :), I have produced a list of all of the Pegasus nominees that were to an existing tune and all writer/composer/performer nominees with a substantial reputation for writing parodies. It's a long list (winners asterisked, one question mark that I'm not positive about):
I observe that we seem to get a fair number of such nominees (and winners!) without having this category on the ballot every year. Rotating it in periodically seems reasonable, but I'd hate to see it eat one of the floating categories permanently, as they cause a lot of interesting songs to bubble into the process.