Hi SepticRevo,
As I suspected, your strategies are NOT where they need to be. You can definitely make some big adjustments between now and July 23rd, but you really need to get on it ASAP.
If you really need a 680, you should be scoring a 700+ on your practice CATs. A 60 point increase in 1 month is pretty darn ambitious, so I'd suggest a total strategy overhaul.
For DS, a "value" and a "yes/no" questions are VERY different and should not be approached in the same way.
For PS, do you ever backsolve/pick numbers? In what situations?
For CR, you need to change your strategy tailored to the Q-type. You would not approach a Flaw, Bolded Statement, or Evaluate the Plan question in remotely the same way. There are built-in expectations for the correct answer in CR depending on the Q-type. You MUST identify the Q-type category immediately and adjust accordingly.
For SC, splits are misleading. Just because 2 choices have 1 construction, and the other 3 have a different construction does NOT mean that is what the question is testing. Yes, you need to look for common errors, but you need to use process of elimination and be clever about it.
RC is my specialty. What do you mean when you say you "read" the passage? There's a million ways to do that. For GMAT success, you have to anticipate the questions and essentially find those answers the first time you read, reading critically and intelligently, ignoring confusing, irrelevant details. Searching and evaluating thoroughly for the author's point of view, the structure behind each paragraph's construction, noting transition phrases, key words, etc. It's so much more than just passively "reading."
Pacing-wise, 15-min of extra time is a waste unless you're getting all the questions correct. Ideally you're answering the final question with 10-seconds to go in each section. Are you working with benchmarks in front of you so you're exactly on track throughout each section?
I'd highly suggest you re-evaluate your strategies with a tutor. Your test date is soon, and while you CAN bring your score up a few points by identifying the content you don't know and reviewing it thoroughly, I don't think you're going to jump from a 620 to a 680 without re-evaluating HOW you approach the questions.
Finally, 100% you MUST MUST MUST MUST MUST (emphatic enough?
) review ALL your GMATPrep exams thoroughly, knowing how and why you got each Q incorrect. They do not provide full explanations, but you can find them easily enough via Google. The GMATPrep doesn't do the hard work for you the way test prep companies will but these questions are worth their weight in GOLD. A lack of review will kill your progress.
It's also possible your strategies rock but you don't have a handle on the tested content or are really all over the place when it comes to pacing. 
