Adam, you ask many excellent questions, and maybe have some of the answers embedded in your post. There have been may pprune posts along the lines of "jet engine efficiency" and while I cannot spar with those of immeasurably more intelligence than myself, I've great interest in this topic. May I humble request that you define some of the terms you use? Specifically;
para 1: "in the name of fuel efficiency"
para 2: "Any prop or fan will lose efficiency"
para 3: "lot of efficiency"
para 4: "more blades are more efficient"
para 5: "increases fuel efficiency"
I've come across "propulsive efficiency", "cycle efficiency", and "energy efficiency" to name a few. Google to view even more. Personally, I like to consider the term "fuel efficiency", which I believe is understood as TSFC, which some may use the generic term "efficiency". TSFC is thrust specific fuel consumption, which is, of course, in American units is, lbs of fuel burned, per lb for thrust produced, per hour. Sounds like a good discussion.