I started talking about BAbip because you are the one who brought it up. I personally don't think it's a meaningful stat. Sure, if you take into account a plethora of different factors, then sure, it is more meaningful... but then again, the other factors are what is giving you full picture, not that BAbip stat.
On 2-strike hitting, I do believe that occasionally a hitter will have a little more success in 2-strike situations than other situtations, but it is rare, and still has more to do with the type of hitter. Guys who rarely strike out (or just swing and miss) will generally have more success in 2-strike hitting situations than the league average.
However, I still don't think that crappy hitters have success with 2-strikes. I'm sure you could find a couple of crappy hitters that had some success in one season with 2-strikes, but i'm sure it's extremely rare, and you couldn't find anyone who sustained that over their career.
I think my overall point is that a great hitter will have more success than average in 2-strike situations, because they are good hitters. Great hitters that don't strike out often will have even greater success. But crappy hitters simply don't have success with 2-strikes. It just doesn't happen. If you can find some statistical evidence (more than just a couple of outlier single-seasons), I'll gladly eat crow.
Also, I didn't know you weren't just reffering to Ortiz with that 2-strike comment... because you were just talking about Ortiz.
Oh and with C. , where exactly did you "prove" that struggling hitters could have success with 2-strikes (and please, don't give me examples of guys like Polanco and Eckstein. 2-strike situations mean far less (short term) with guys who only swing and miss 7% of the time).