I'd be inclined to allow it, though I'd propably follow the idea presented with the variant to combine it with the thug variant.
Anyway, I don't have the appropriate UA so I can't help you on the fighter stuff. I would be careful of doing it, but as the above poster said - if they are different enough it could be legit.
...it seems to me like someone who did that would be trying to cherry-pick the feats from the first Fighter levels and the Sneak Attack from the first Fighter variant level while retaining full BAB in something like Fighter2/SAFighter1.
Think twice before you allow this multiclassing because otherwise you are offering something more powerful than allowing the Fighter to swap out any one bonus feat piecemeal for Sneak Attack.
Can you explain what you mean here?
New Feat said:Sneak Attack [Fighter]:
The Fighter gains 1d6 Sneak Attack damage or her existing Sneak Attack damage increases by 1d6.
Special: This feat can only be selected as a Fighter Bonus Feat and cannot be taken in any other fashion