I guess my reply is a bit late but I will just keep it here in case there is a future need for someone in the similar shoe.
My case is rather special, I only took up PR (student scheme, NS-liable) after I grad from JC last year and done my NS registration in March. From there, my story of continual nagging CMPB starts...
Of course, I do have a sound ground to request for early enlistment: I secured a UK university for 2020 intake (which is quite rare actually because they usually only give one-year deferral) and also a government scholarship for that study.
Therefore, what i did is that I call CMPB to get my medical screening re-arranged to Mid-April, while the earliest slot shown on my portal is Mid-May. I then right after the check-up, emailed CMPB to beg them to expedite their process of assigning a medical grade, which they managed to finish within half a month, which is way faster than the normal one month.
However, after that, my concern further rises because it seems many poly batch people already got their letter in Apr and I scare that there might be no vacancies left. I then kept calling CMPB: once every 2 days, and even emailed to their boss (well you can find his email address/phone number online, but if you dont take the initiative to check, you dont get it) and boom, one week after getting my PES, i got my date and letter. The date was even pushed forward after i re-passed my IPPT (my school result expired...)
So my conclusion: IF YOU WANT TO GET THIS THING, YOU HAVE TO TAKE INITIATIVE TO REQUEST AND TO ASK, INSTEAD OF ASKING PEOPLE BLINDLY ONLINE.
hope that helps