Can I just comment that you are not pulling back on the elevator in a tail stall to try to unstall the tailplane - you're puling back on the elevator to try to get some nose-up aircraft motion, because with the tail stalled the aircraft will be nosing over like mad if you don't.
To unstall the tail you need to reduce the AoA at the tail - which is achieved primarily by selecting wing flaps up and reducing the downwash over the tail.
The normal effect of flaps on an airfoil is to reduce the AoA at which it will stall (you're making the airfoil work harder, so you'd expect to have it "give up" sooner) - although the maximum lift for the flapped airfoil does increase. I would therefore be shocked if any of the cases cited used flaps ALONE to recover; lowering the AoA has to be part of stall recovery.
What lowering the flaps will do, in combination with a lowered AoA, is enable you to generate more lift once you're unstalled, so you'd need to lose less altitude to recover back to a safe flying speed. I don't know, but I'd think that's the reason for flaps selection on some types - to make the recovery better.