Basically, any weapon that's mechanically in the same pay-grade as a rapir (e.g. a longsword, scimitar, broadsword, battleaxe--heck, just about any military one-hander) isn't any kind of game-changer at all, just a variant. It's only when venturing into two-hander territory that trepadation is in order, and that can be addressed by diminishing the benefit of sneak attack. If CA is indeed easy to get, then watering down sneak attack would represent a genuine trade-off that keeps the overall damage output within reasonable bounds.
I'm... not sure I'm actually in disagreement with you, here, as that's pretty much what I was saying up thread. I'm hesitant to say that there should be an official feat allowing this, just cause I haven't taken a close enough look to see if any abuse if possible, but I think its the sort of thing I'd be perfectly fine with as a DM.
Let me try and address the original question where, I think, some of this debate seemed to spring from:
Let me put it likes this: why would any of this be a potential problem for the rogue, but not for the slayer? The latter class gets a non-conditional, unlimited usage +1 to hit and Dex bonus to damage on all of his attacks. His stances give him access to bigger damages than thse stances afforded the thief.
So, let's say for the sake of simplicity that using a non-sneaky weapon like a fullblade loses a die of sneak attack. At the heroic tier, he's getting an extra 1d6 3.5 points points of damage. The slayer easily makes up almost all of that with his Dex bonus, and as a consolation prize for the remainder, he's got superior AC and HP.
I think this was where most people objected - you seemed to be treating the Slayer's damage bonus, since it was 'always on', as being in a different category from Sneak Attack. I just don't see it that way, and think very few do - Sneak Attack, Hunter's Quarry, Warlock's Curse, Sorcerers adding Str or Dex, and Slayers adding Dex - these are all the classes core 'striker mechanic'.
Now, Thieves and Slayers tend to get some extra bonuses, largely to compensate for lack of dailies. The rogue tends to get ones associated with skil abilities or with damage, while the slayer gets ones that boost durability and mobility.
It does become hard to directly measure some of these different specializations... but I think in terms of raw damage, the thief already tends to come out ahead of the Slayer. Partly because he has more options for feats to boost damage. Backstabber is a pretty big one - but you can't dismiss it, because the Slayer simply doesn't have any equivalent feat. Giving the thief another feat that could potentially boost damage by several points, when the Slayer doesn't have any such options... I don't think that would be reasonable.
But offering a feat that allows an upgrade to a bigger weapon at the cost of a die of sneak attack? Where the rogue's max damage essentially stays the same, but they now are more viable without combat advantage (as well as allowing more concepts to be explored?) I think that's perfectly viable, especially in a home game.