First, yes, a 690 is a really good score. I know you want more, but I just want to make sure to give you credit for that!
Your 1st and 2nd tests were only about 3.5 weeks apart—it's not unusual to see the same score in that timeframe. So I wouldn't think of it as having underachieved on that second test. It was worth trying to see if you could get there and not have to study anymore—the test has a standard deviation of 30 points, so your goal is within 1 SD of your first test score.
But I wouldn't advise you to go for 3-4 weeks this time. I'd give yourself maybe 6-8 weeks. Again, it could work in 3-4 but you might just find yourself where you are right now, with another month gone. You've tried that once; now it's time to try something different (as you noted in your post).
Before we dive in, you may qualify for a Post-Exam Assessment, depending on what program you did. The PEA is a free one-on-one meeting with an instructor to debrief from the official exam and set up a plan for your retake. If you didn't already do this after your first exam (only one comes with the program), email our student services team at
gmat@manhattanprep.com to see whether your program qualifies for this and to sign up, if so. (If you took any full course or did the full Interact program, you qualify.)
Overall, the highest Q score is 51, so you're 4-5 points below the peak. The highest practical verbal score is 45 (it's really rare to score above that), so you are 7 points below that peak. So there's a little bit more room for improvement on the verbal side.
But let's couple that with your comment that you're targeting Q 48 and V 40, based on your official practice test scores. First, the most common scoring combo out of those two subscores is a 710, not a 720. See here:
https://www.manhattanprep.com/gmat/gmat-score-calculator/If you can get Q up one more point (to 49) or V up one more (to 41), that's more likely to get you the desired 720. Either way, you're looking at trying to pick up another 1-3 points on Q and 2-3 points on V. So this is pointing to spending roughly the same amount of time on Q and V—or maybe even a slight edge to V.
Next, you said that, for your second exam, you reviewed advanced Q and SC concepts (right? you said "sentence comprehension"—I'm guessing you meant sentence correction, but you could also have meant reading comprehension). And you did a bunch of quant problems.
Did you not review CR and RC at all (or very little)? And was most or all of your problem focus on Q—not SC?
Did you get the Enhanced Score Report for either of your official exams? Costs $30 but can
often provide data that's useful to help you figure out what to do for a retake—though not always all that useful. See this article for more detail:
https://www.manhattanprep.com/gmat/blog/enhanced-score-report-part-1/I'm guessing you haven't because you didn't share that data but, if you have, please include the data in your next post. I'd be happy to analyze / tell you what I think.
Big picture: If you feel like you're spinning your wheels / not sure how to dig in and improve at this stage, then yes, something like tutoring or the Advanced course would help. That of course means spending more money and I have a conflict of interest in recommending something like that—so I'll just say that these kinds of solutions are useful when you feel that you've hit a wall and aren't sure you can come up with effective ways to push yourself to that next level.
If you qualify for a PEA and haven't done it yet, sign up for that right away. If you think you might want to do some tutoring, you can tell our student services team and they'll try to pair you with someone who has tutoring availability—so you can meet for free for an hour to see whether you connect well enough with this person to want to spend money on tutoring.
The next Advanced course starts in 9 days (and that program runs for 5 weeks, which is probably just right for your timeline). There's a significant discount if you've already taken the regular course—ask our student services team, but it's like half off or something.
So I'd try to get the PEA in ASAP (assuming you're eligible) and then you can decide how you want to move forward. (Note: It can take up to a week to get the PEA scheduled, so put in the request right now—gmat@manhattanprep.com.)