If you want to keep that look, most people rip down the nose and sister up some wood prior to capping.

+1 to WoW's comment. If you want to use pvc instead of wood that should be doable, just make sure that you get all of the rot so that you have something solid to secure to, and that everything is properly caulked and sealed.

Thank you WoW (I've heard good things about you in this forum multiple times...).

I understand what sister means when it comes to joists, but are you talking about adding a sloped piece of wood to fill the void, or cutting off the nose enough so you can fit a piece in vertically?

Cutting off the nose and ripping a piece of the PVC lumber to fit the removed section and gluing and screwing them together.

Are the windows being capped? Might be easier if you are doing that as part of the install.