You should focus more on the soft aspects of your app, as your stats should be fine for our state schools. Your GPA is strong, and your MCAT is reasonably competitive already. A 507 equates to around a 29 on the old test and puts you at about the top quartile. I agree with gyngyn that you shouldn't retake the test unless you are doing significantly better on your practice tests.
Also, you need to apply early this time. Early means being verified in June, not in August. All of our state schools are rolling, both for admissions and for interview invites. The later you apply, the fewer invites are left to be given out.
I like your plan to apply more broadly also, including to DO schools.
When you ask your recommenders for letters, make sure to specifically ask if they can write you a STRONG letter. The fact that you got no invites at all last time suggests that there may have been a lukewarm letter in the bunch. Make sure to have someone critique your PS as well, as this could have also been an issue.
To answer your question, no, I don't think you need to shadow on top of scribing, although you may need to spend some time shadowing a DO in order to get a DO LOR, which is required by some DO schools.
Hope this helps, and best of luck with your apps. 🙂