I would advise you apply for it right away. I was able to do so without the PCC request from NDVO which was worth the risk and it worked out quite well. All I did was to use the PER mail as a proof and mention that my application was In process and hence the need.
1) Just drop them a mail (SPF_CID_COC @ spf.gov.sg ), provide them details of your stay in Singapore, FIN/ PP No whichever that you do have, and your reason for application.
2) Expect a response from them (give them a weeks time) with details of the COC Appeal Form and the COC Application form, reach out to them over the phone if you see its taking more than a week which was in my case.
3) Fill up the forms and submit all the necessary documentation and send it across by snail mail and you are good to go. You can expect the entire process to be complete in about 30 to 45 days. You can always follow up on your application by reaching out to them, they do give you a reference number.
They are also accessible over the phone and were very helpful to all my queries. You should be able to get the numbers from their website or elsewhere from this forum , which is where I was able to find them. My current phone's gone for a toss sadly, else would have been able share them with you.
All the very best bro!!n Cheers!!