A couple of days ago, I was skimming an article about an experiment intended to determine whether the Universe is merely a hologram, and tried to conjure up "What you mean, merely a hologram?" in, of course, Arnold J. Rimmer's voice.
Somehow, though, the voice I came up with was Sheldon Cooper.
Apparently there hasn't been a Red Dwarf crossover episode of The Big Bang Theory, though Sheldon has a complete set of Red Dwarf on DVD.
This must not stand!
Try this on for size: a sort of reverse-Back To Reality.
We need Wil Wheaton, obviously. In his Wesley-with-a-beard guise, he slips the regulars a dose of an experimental telepathy drug, causing a group hallucination*. As they'd just (finally) binge-watched Sheldon's complete set of Red Dwarf, or at least some portion thereof**, they find themselves in an all-new episode....
Sheldon must be Rimmer; he's a perfect match. This makes Leonard Lister.
Howard has to be the Cat, given how hard he tries.
This leaves Raj as Kryten. Can you imagine Raj being Kryten? The personality, the selective mutism: he'll do.
Penny must be Kochanski - the original version, not the parallel-universe one nor Rachael. This fits perfectly with Leonard being Lister.
I'll leave the story-within-a-story to your imagination. What, you think I'll do everything for you?
* Alternatively, they could be tired and slightly drunk, and under the influence of one of his infamous suggestions that such a drug exists.
** Actually, they should only have watched the first few seasons. Mustn't get far enough along to meet New Kochanski, or it gets confusing.