Kingston- I think you may be reading this wrong. Lets break it down...
"This unassisted segment MUST include a flipping toss into an extended 1-leg AND/OR 1-arm stunt with a flipping or double twisting dismount. Any other stunt segment must be majority unassisted."
The first part is, "This unassisted segment MUST include a flipping toss into an extended 1-leg." So, this would mean a rewind land-in stretch, or bhs up land in stretch (both flipping into immediate). Notice no full ups in this category. Must be 6 stunts (if there are 20 people, that is).
The second part is a continuation of the first part in talking about the flipping mount- "AND/OR a 1-arm stunt" (as opposed to 1-leg). I interpret this as a rewind awesome, or bhs-up awesome.
The last part is for BOTH the first and second part, which means you must have a flipping dismount or a double down. So, you basically have to have a flipping mount (rewind/bhs-up), and it can either be into an immediate 1-leg (land-in) or 1-arm (awesome)- your choice. The last part should actually be another sentence, which is a bit confusing. It really should read, "both of these stunt options must include a flipping or double twisting dismount."
Does this make sense? I think you were combining the second and third part into one part, which would make rewind awesomes useless. I dont think thats what they intended, just not really grammatically efficient.