An old Twitter post from Derek Yu suggests that the "Sorry, I'm Dead" guy is based on this old monster toy from Bandai, which was released a year before Monster Party. It's from a line of toys called "Gegebo Majyu".

Hmm.. one thing that's puzzling me is that the translation seems different then the one I've seen elsewhere. Compare this bit from the opening. Left is version uploaded by CDRomance, right is a screenshot from the Romhacking.net page.