Hi ManSab,
To start, Test Day is a rather specific 'event' - the details are specific and they matter, so you have to train as best as you can for all of them. The more realistic you can make your CATs, the more likely the score results are to be accurate. The more you deviate, the more "inflated" your practice scores can become - and that's likely what has happened with most of your CATs. By skipping sections, you've been taking shorter Exams that required less effort and energy from you - so most of your scores are likely not completely accurate. If you did anything that was unrealistic, such as taking the CATs at home, taking them at different times of day, etc., then your scores might be more "off." This is meant to say that you should plan to be a bit more rigorous about how you take your future CATs.
If we assume that the 620 is accurate, then you're going to need to learn/practice some new Tactics in both Quant and Verbal. Given the 'book-heavy' study that you've done over the last 5 months, you would likely find it beneficial to invest in a GMAT Course of some kind (either Guided Self-Study or instructor-led). Most GMAT Companies offer some type of free materials (practice problems, Trial Accounts, videos, etc.) that you can use to 'test out' a product before you buy it. We have a variety of those resources at our site (
www.empowergmat.com). I suggest that you take advantage of all of them then choose the one that best matches your personality, timeline and budget.
If you have any additional question, then you can feel free to contact me directly.
GMAT assassins aren't born, they're made,
Rich