580 is almost close to 60th percentile which is a good score. Taking more mock tests won't help you any good unless you have timing issues. You haven't provided your individual scaled scores of actual/mock/GMATPrep tests. They are ones which will help you to reach your target score.

scaled scores: Quants (47), Verbal (23). None of Kaplan test scores were below 600.

First of all its better to take GMATPrep tests as much as possible. Other practice tests are close to GMATPrep but not a very good indicator. Do not rely too much on other practice test scores. To know where you stand you can count only on GMATPrep. To know where you want to improve you can rely on other test prep companies to a certain extent.

For 700 you need to score Q47-50 V38-35.

If you haven't studied much for quant then you have room for improvement. Any advanced practice material with good knowledge in inequalities/word problems/statistics/probability/Combinatorics/geometry will help you reach 50. If you had already put in much effort you can improve it to 48 49.

You have lot of room for improvement in verbal. Anything less 30 you are too weak in one section and not conceptually strong enough in other sections as well. Take GMATPrep tests to know which section you make more mistakes. You have to equally good/strong in all sections.

RC:

One of the most important section. Check your GMATPrep tests to know how many mistakes you make in this section. There will be 4 RCs with 13 questions. Anything more than 4 mistakes then you have to work hard.
You are making more continuous mistakes because you are making more than 1 mistake in 1 RC where 3/4 questions come together. OG passages will do. Try to see Ron's videos. They are good. This is my Achilles heel.

CR:
OG problems. Powerscore bible to know the different types of questions. Don't get too much involved in powerscore as it might have detrimental effect on your CR performance.

SC:
One of the easiest section to improve. MGMAT SC is the bible. Read it two/three times. Practice less review more.

Whenever you work on any section try to work on the most tested concepts say strengthen/weaken in CR, parallelism, modifiers in SC. Get strong in those first and then you can work on weak topics. Take a mock once a week and keep track of your improvement. Hope this helps

Since you cite timing as an issue, I absolutely recommend:

1) regular full-length tests (without letting the score worry you much, since their predictive power is limited). More than two in a week is usually a mistake, since you should also be reviewing them thoroughly
2) an error log, which also tracks how you do when you narrow questions down to two answers