How To Insulate A Bay Window

Question

I have a 1929 craftsman house. The dining room has a bay window, original to the house, cantilevered outside the foundation. The floor joists were covered exterior on the bottom with tongue & groove flooring, then the interior floor cutting abroad to utilize the joists equally a cold air return. The wall is 2x4 stud, plaster & lath inside, forest lap siding outside, filled with diddled polyiso foam thirty years ago. The forest lap siding was topped with 1/8" greenish cream sheeting and vinyl siding in 1992. 1/2" styrofoam sheet (small white beads, like in a cheap cooler) was added nether the window, almost probable at the same fourth dimension as the vinyl siding in 1992. The rim joist under the window appears to have merely the ane/8" green foam, vinyl, and lap siding roofing information technology, no other insulation.

I recently establish the styrofoam under the bay was only press-fit in some areas, no fasteners, held upward by a friction fit on the back side of the lap siding. This left air gaps on both sides of the lap siding, between it and the styrofoam on the backside and the greenish cream on the exterior.

I recently obtained a pile of ane" styrofoam panels that I would similar to use to cover the existing ane/2" styrofoam on the lesser of the bay. To cutting drafts, I would like to install it all the way out to the vinyl siding, screw and caulk it in, closing the air gaps around the lap siding.

I can imagine this would close the drainage path behind the vinyl siding, if the green foam wasn't there every bit a h2o barrier. I can besides imagine closing the gap behind the lap siding could possibly reduce air menstruum and drying to the outside, only the wall nevertheless has plenty of air flow inside.

Question... Would adding more styrofoam nether the bay, closing the air gaps at the bottom of the lap siding & behind the vinyl, or insulating the inside of the rim joist (inside the cold air return) exist a bad thing? Can I close these gaps or should I leave them for drainage & airflow?

Edit: Added 1 pic looking in cold air render register, showing the rim joist fastened to the cease of the floor joists. The floor joists are covered underneath with tongue & groove flooring (outside) and sail metal (in the basement) to create the common cold air render for the furnace & a/c. The smooth surface between the floor joists is paper-thin laying loose on elevation of the t&g floor.

Besides added two pics under the bay window showing the white vinyl siding, one/8" green cream sheet insulation, brown lap siding, heavily weathered white trim board, and 1/2" white styrofoam.

inside the cold air return, showing the rim joist