well one thing about "Therefore we have: 15/3.724 = 4.028!" that is true of mongoose, so for SH you get 4 hits while mongoose is up but only 3 if SH has executioner. so mongoose in that case works well with SH i would agree.
if you are being focus'd mongoose isn't going to save you... in the 11k+ range which most warriors are the extra 240 or w/e it is really isn't going to matter.
2ndly, i have mongoose on my 1h'er, and if you are being focus'd as a warrior at any point you should have a shield and be in D stance. believe me i do it around 80% and to no end it really irks people lol. however, for simply bursting things down i have to say executioner. we did another 50 or so games last night on a new 3v3 team. to see me critting rogues for 2500, 3k+ MS's on mages. its just a difference which is hard to account for.
and i tested it with the trinket
http://thottbot.com/i28121 which i had spoke about earlier. in total dropping about 1700 ac from my enemies. huge difference.
so overall i agree with almost everything you said, but put it into perspective: armor and dodge are nice for defensive, but should be on your 1h'er to tank when being focus'd not your 2h'er.
mongoose increases attack speed yes, and 2% on a 3.8 speed is a lot, but with flurry or a thundering meta or dragonspine trophy, 2% of ~2.5 - ~2.8 is even less. the 3.6 crit is nice, i will never doubt that, but think about the axe spec vs mace/sword spec conversations we have also been having. how do you not see mongoose as another way of saying axe spec.
short of doing a lot of testing and numbers of my own (sadly i dont anymore, i troll the forums at work and play when home, i rarely spend what little play time i have to do testing) i can tell you executioner works and has impressed me quite a lot since i switched to it.