Quantitative Reasoning

Need your advice - do you think this is even possible?

I've studied on my own and have only nominally improved my quant score from 37 to 38. (I am in the 73rd percentile for verbal and 5.5 for essays). I need to take the test in late May or wait until the next round and take it in mid-July.

My dream school "encouraged" me to reapply (paraphrased):

The Admissions Committee has decided that your current GMAT score does not correlate well with the overall quality of your application, and we would therefore request that you retake this test...Although this is a final decision on your current application, it is above all a letter of encouragement and should not be seen as a rejection. However, we strongly encourage you to reapply as and when you have a higher GMAT score... The Admissions Committee has seen potential in your application, but would like you to strengthen the above-mentioned element before reapplying for admission.

I tutored statistics in college (but years ago), I've always done well in math. I've never taken a class or had a tutor for any standardized test so there are definitely things that I can be taught. I'm checking references for a private tutor right now. There's no way I'll tackle it alone - I should have learned that for my second time around.

Am I crazy to attempt it? This school is my dream school and I am laser-focused on getting in and maybe I am not thinking this through. Is it possible to improve my score by 20 percentile points with tutoring and hard work, or am I being unrealistic???

Be honest.

Have you done this and succeeded? If so, what do you recommend? I have 2-3 months to achieve it.
Have you done this and failed? What went wrong? Would you do it again?
Am I crazy to attempt it?

Thanks.