I don't think there is a right or wrong answer, but I personally wouldn't waste a day taking a diagnostic exam at this point since you're short on time. There is no exam that is comprehensive enough to truly show all of your strengths or weaknesses, so I don't think it's worth spending time to do one in your position.
Work through all of the aamc material and use that to guide you study. Schedule out each day and what you need to get done right now so you can ensure you fit it all in. Use khan academy for psychology and memorize every term presented. Any concept that presented multiple times in the AAMC needs to be deeply understood.
Even if you do all of this, getting a 515+ is not guaranteed at all. Typically it takes a few months of improvement and learning over time to get to that level. The exam has shifted from just rote memorization to more analysis and it takes a lot of time typically to learn these analysis skills, so that's why it's difficult to get to this level in such a short time period. I wouldn't discourage you from trying, but as you get close to the exam, if you aren't particularly close to your goal score, I would potentially think about postponing the exam.