I assume Traupman's reasoning is that he's trying his hardest to differentiate pajamas from other types of clothing you might wear at night. He defines
synthesis as "a set of matching articles; dinner service; (matching) dinner clothes," which picks out a special feature of pajamas as a matched pair of shirt and pants. The main problem I see with this isn't that the term is Greek, but that there's a bit of an open question about what syntheses actually
looked like, which makes appropriating them in a modern context doubly questionable. The diminutive would also be a mouthful;
synthesicula perhaps?
Of course, if classicism simply isn't a priority for you and you want to be completely unambiguous, you could just borrow the term from Hindi or English and get
paiama ("jammies" being
(pa)iamella). It's got no historical standing at all that I know of (though Vicipaedia seems to like it), but it all depends what you're using the word for: If you're writing a pop song in Latin or otherwise want something short that exactly differentiates this article of clothing from all other vestiments of the night, it's at least declinable. It's the sort of term you'd expect if Latin were a living language, with all the corrosive borrowing that must accompany life.