OK, I recant and denounce myself - the idea that any sensible variation of the Sleeping Beauty problem must have a 'canonical' answer is wrong, and FNC is broken.

Very admirable stance to take :-) I wish I could claim I found the problem and immediately renounced SIA and FNC, but it was a long process :-)

Btw, a variant similar to your alpha to gamma was presented in my post http://lesswrong.com/lw/18r/avoiding_doomsday_a_proof_of_the_selfindication ; I found the problem with that in http://lesswrong.com/lw/4fl/dead_men_tell_tales_falling_out_of_love_with_sia/