Hi Banzai. Kaplan Premier is a solid strategy guide but its not spectacular, and you are seeing that with the explanations and concepts sometimes lacking. The
MGMAT series is better and deeper, and you won't run into issue like that with it. I recommend it.
For practice problems, the OG 13th edition and the Verbal and Quant review books are pretty much required. They are excellent practice problems, very similar to the official test because they are retired official problems.
What are you scoring now on CATs? That will put your 620-650 goal in perspective. The test is scored in units of 10, so a 625 would be a tough score to earn : )
I've written a guide on how to self-study that could be really helpful for you:
GMAT Clarity (amazon link).