The short answer is no. There are of course ways to do it, but not directly with your current reservation.
If you were staying at a DVC resort then you could try renting points for your reservation instead of booking through CRO. In this situation you would ask the DVC owner to add the dining plan to your DVC reservation. You would pay the owner for the reservation and you would pay Disney for the dining upon arrival. I see that you're staying at the Polynesian but if you're willing to switch to BLT (closest DVC resort to Poly and also on the monorail) or another DVC resort then this could work for you.
Your other option is to book an AP package reservation. You can not use your PIN for this; you'll need to use whatever AP discount is currently available. You can book an AP package even if you don't have the AP yet. I've read different things about the requirement for having the AP at check-in. Some people say that as long as you show the AP at some point on the same day after you've checked in that you're fine and others say that you need to go to a Guest Relations window first to get your GAD and upgrade it to the AP before you check into your resort so you can show the AP at check-in. Personally, I'd plan to get the AP before checking in just because I'd be too anxious that there might be problems at check-in if I don't already have it. For your dates written in your signature, the AP rate is 42% off so even better than your PIN. I just checked the passholder site and I am not seeing any availability for Polynesian meaning I don't know if this is actually a viable option for you. There's no availability online but you could always try calling in to see if a CM can find availability that's not showing online.
