Insulation repair

My house has two bay windows that are poorly sealed and insulated (they allow some very cold air into the house during the winter). It appears that the vapour barrier in the floor joists is eith leaking, or perhaps never even put in place.
The windows extend out beyend the foundation of the house, but there isn't enough room to get underneath them to re-insulate and re-seal. Even worse, I have hardwood flooring on the inside, so I really don't want to rip it out to get at the space between the floor joists.
I am planning to remove the exterior siding and sheathing to get access. I haven't done this before, so I need to ask -- is this the "best" way of solving the problem? Or am I overlooking something obvious?

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