I guess that could be seen as a reference but I'm thinking about something more along the lines of a specific character being referenced, or a song being remixed (like that other one, you know the one, spoilers).
I dunno, but the paper plane and turning sideways abilities seems more like a general paper gimmick to me... maybe I'm just being too picky...
Like you said, the game misses the point of a crossover. This game could be a celebration of the two series' entire legacies but so far it just seems to celebrate sticker star.
What I would've loved to see is, instead of rescuing a ton of generic un-named recolor Toads, why aren't we saving characters that we already know and love?
Like, if they have to be Toads why not Miss Jolene, Tayce T., Zess T., Chanterelle, The Excess Express Conductor or Engineer, Heff T. , zip Toad, Russ T., Vanna T., etc.
But they don't have to be toads. There are a million other Paper Mario characters that you could find instead.
...I guess that wasn't in the budget...
...or maybe they really do wanna retcon the old Paper Mario games as non-existent or not canon...