Forget the past month and just look at the last 2 weeks--during which the Sox took 2 of 3 from the Cardinals (who were then leading the NL Central Division) and 3 of 3 from Cleveland, who were then leading the AL Central Division.
About those bottom feeders. The very worst team in MLB, the A's, wins 1 out of every 3 games, but the Sox took 5 of 6. Detroit wins 4 of 10, but the Sox swept 3 of 3. The Angels win 5 of 10 (46.8%), and the Sox took 3 of 4. Seattle, almost as good at 46.1%, lost 2 of 3 to the Sox.
What I will agree with is that the Sox so far have struggled against all four of the other AL East Division teams. Not just the Yankees, Rays, and Jays, but also the Orioles, who have taken 4 of 7 games so far. And, as you imply, this could well doom the Sox, but I'm not yet ready to go there.
As for the Jays, let's not forget that playing in Toronto has removed our newly crowned closer, Houck, who has the Sox 5 most recent saves. Plus Duran, for whatever that's worth. And Sale, if he ever returns.
Indeed, this morning I read a comment that it's quite possible the Sox could play the Jays in the postseason at Toronto--without Houck, Sale, Duran, whoever.