Mortimer has a balance to maintain: keep keen thinking he's dead, but also keep certain people aware of his presence while he's up to no good. I think its a safe bet that, at the minimum, he's got an android at home to keep his family busy.
I've always thought that the android on Vorticon VI was there to rule the Vorticons while the real Mortimer was out working on his bigger and badder scheme, the omegamatic.
I'd bet that the helmet being on the Omegamatic is a clue that it WAS the real Mortimer aboard; seems like an android wouldn't take off the helmet (if it even could). Perhaps a message from the makers that "Keen was this close to catching Mortimer this game! Come back in "The Universe is Toast" to finally get him!"
You've mentioned your version of the story several times, I'm curious if you have anything planned for the 'complete story' it sounds like you're developing
Perhaps he left the note behind because he felt like it's time Billy learned he's still out there...maybe because Mort's ready for him...or because he wants keen to try and fail. Mort would surely hate him after ruining so many plans.
I think these are all ego related though. I mean, wanting Keen to know he's there means he wants attention, egomaniacs want attention, want people to know how great they are. Wanting keen to try and fail, the only motive i can think of suggests he only wants to prove his superiority, the ego strikes again.