Champions predates Rock You by at least two years.
Bicycle, IIRC, also predates Fat Bots according to what's been said.
White Queen (at least lyrically) comes long before Black Queen.
Flick of the Wrist (and the rest of the SHA album) would also be pre-NIH.
As for writing in similar veins, they did it all the time: Body Language vs Dancer (well, so so), Princes of the Universe vs Gimme the Prize, The Hitman vs Headlong (in some aspects more than others), plus a bunch of songs on which they collaborated (Show Must Go On, Bijou, Mother Love).
John hated HS. Frederick's favourite singer was not PR. Roger didn't compose 'Innuendo.' Witness testimonies are often inaccurate. Scotland's not in England. 'Bo Rhap' hasn't got 180 voices.