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It sounds like it would be a good idea to weigh down or brace the floor (the portion that is there now) while pouring so it doesn't push it out. I would stick with small batches so you don't build too much cumulative pressure.

If you get most of the foam in and wind up with a few spots that need additional foam, or it bulges above the edges, it is not too difficult to add a small amount and sand it to shape even if it is curved. Once you have most of the shape from using the the cut out floor piece covered in plastic, it will probably be pretty easy. I had to fill all curved areas and was surprised at how I could shape it.

Long boards help a lot including for curved sections, both to sand and identify highs and lows. I used two long boards, one slightly longer than the open section, which I placed over the length of an open section to measure the gap between the height of the foam and surface of the glass, and one just shorter than the the open section to tell where highs and lows were on the foam. I placed the boards not spanning a curve, but along a horizontal line, like placing a board length-wise inside a half tube.

Hope I am not adding too much detail. But I spent a lot of time recently on a pretty similar situation. At least your boat is light enough to move by hand. Good luck.