I just finished Kaplan content review and took my second ever timed test FL 2 - 497. My Diagnostic was 483, so I was in exact same position as you.
First of all - finish your content review. That took me 2,5 months. And that is only first run, as I'm sure there's tons of details I've missed. I'm going to hone it down while doing FL's.
Secondly, don't get discouraged, content review is just 50% or even less of MCAT success. The rest is practicing. When you'll finish content review, start practicing FL's - every 4th day. So during 1 month you'll cover at least 8-9 FL's. In between FL's during the rest 3 days do - mistake review with going back to content, do AAMC Q's packs and do Q-bank and section/passage based questions. Also watch videos on topics you made mistakes and your weak topics. During next month do EK FL's and AAMC FL (last). I can guarantee that in 2 months studying (after been done with contetn review) you will be somewhere close to 505 or so on Kaplan, which means more on real test. So in total it takes 3-4 months - but it's expected to be like that coming from 483 to around 505 (I'll assume a bare minimum you want to be).
If you want to make it happen faster - then you can study more every day and do FL's every other day, but there's limit to our capabilities and I don't think it's possible (for majority of us) to improve from that low as 483 to 505+ in less than 3 months no matter how you cut it.
P.S. If you are trying to keep with Kaplan course schedule - don't even try - it's crazy fast pace and they did it for those who review material NOT learn it for the first time. I was learning it for the first time and so I did it in my slower pace. Your 3 weeks is nothing yet, so keep calm and continue read and practice.