I passed the OCMJEA earlier this month. Before my memory got stale, I made it a point to write about my experiences with the OCMJEA part1/2/3. I have written about it in length and these are going to be "longreads". The links redirect to my blog.
#1 You mentioned that the assignment may take months or several months. I disagree. It should not take more than one or two weeks if you are prepared and experienced. Understanding the problem is the key, solving it the right way should not take long.
#2 You should be prepared well before taking the essay exam. You should not be writing till the end. Short and crisp but effective writing should get you there.
#1 My assessment was that the problem understanding and the documentation of the assignment should take a month (or months). I believe there is no single set timeframe one can achieve this in. If someone works on it 9-10 hours a day, the whole thing can be done in a matter of weeks. But I do understand what you are saying and I will make it clear on the post with an update.
#2 As you said, short/Crisp writing should suffice for the essay exam. I will update the post to reflect that. About the preparation I only meant to say that immediately after you submit the assignment is the time when you are best prepared to give the essay exam (compared to, say, taking a break of a couple of weeks and then giving the essay).