Do you happen to have the AAMC self-assessments? I really like EK, but those end-of-book exams for the science chapters just aren't representative for a couple of reasons: 1) they're too short to properly cover more than a couple of topics within each concept and 2) their scoring system is kind of weird. Basically, keep doing them to make sure you're retaining knowledge from the chapters, but my advice is not to score them at all.
As for verbal, I agree with many others about the EK 101 Passages book - they're very different from AAMC passages. They tend to be shorter, more conversational, and more "word-for-word" (as in, they contain fewer of the tough application/inference-based questions). Since you don't have a ton of time, maybe you could get the verbal SA instead and break it up into chunks of 4-5 passages? Then, at least most of your practice will resemble what you'll see on practice exams.
In general, is it possible to raise a verbal score from a 6 in about a month? It'll be tough, but absolutely not impossible in your case for a couple of reasons. First, that was your first timed AAMC exam. If you were averaging a 6 on your first few tests, that would be a different case, but you truly can't get an idea of where you stand until you've taken at least one or two more. Spend the next month analyzing the AAMCs above all else, and you'll give yourself the best chance at a big score jump 🙂
Good luck!