I think consensus says read TPRH, do problems from BR, and take as many FLs as you can with thorough review of each.
Six weeks is a REALLY tight cram - I'm a month out from my exam (4 weeks), and if you told me two weeks ago to start studying, I'd cry. There's just a TON of material you need to really master.
If you say you're a terrible test taker (like me), then you need to do as many practice problems as you can. It isn't like magic for your scores to increase. It takes a TON of work behind the scenes. Sometimes it's content-based, but many times, it is strategy-based. I think 6 weeks to review all the topics is not going to give you enough time for passages and review.
I quit my job to study full-time, and I'm taking 3-4 months to get it all nailed down. Everyone is different - I hope it would take less time for you!
Not trying to be pessimistic, but just trying to give you insight into how long it can all take. Shoot for worst case scenario. I wouldn't rely on just ONE exam to decide on whether you should shoot for August or not. Besides, to study HARD from now until August would burn you out.
I also think you'd DEFINITELY benefit from having A&P under your belt. The MCAT has a few "heavy" A&P concepts (i.e. the loop of Henle will be your best friend by the end of all this).
I think that maybe a September date would work better - but you'll need to register soon! As someone already mentioned, seats fill up quick! However, I'd suggest waiting a little bit longer - maybe January would be wiser, and you can apply next cycle. Though deferring is so much easier than doing the app process later, during your recovery period.