Since guests that are not staying on property can now make FP+ 30 days out, it might not affect your FP+ if you change your reservation. What I would do is make the new reservation and add it to My Disney Experience before you remove the old reservation.
However the system appears to be adding reservations automatically to MDE so it might remove the reservation too. I would definitely call the number regarding FP+ on the MS website and ask before you do anything. Maybe they can just move the FP+ over to the new reservation.
Thank you for the good information. I'm not within the FP+ window yet, but since I have enough points to book the new reservation before cancelling the old one, I will book and then link to MDE as you suggested just to be sure.