to hover takes a given amount of work and the reaction for that amount of work will be the same irrespective of the prop selected
Respectfully disagree. Some props will do the job more efficiently. A prop that has lots of drag for only just enuff thrust in HOVER ( a high pitch prop like an x-8 ) will force the engine to WORK much harder to generate the req'd thrust for hover.
Don't confuse the work done by the engine with the thrust. That ratio will vary GREATLY with the variables of pitch and speed.