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I have been dealing with foam and a large open section on the bottom of my boat this past two weekends. One technique that worked well was to tape a layer of plastic tightly over the whole open area and pour foam underneath. The plastic spreads the foam evenly and puffs up slightly higher than the edge. I then sanded it down to level. In cases where it was low, I waited for the foam to cure a little, peeled back the plastic, and poured a little more.

One thought is to remove a second panel in the bow before doing anything with the sides. Most of the remaining weight could be in the bow floor, it seems easier to replace floor foam than gunnel foam, and the weight distribution of the remaining water would be more balanced. You could try it and weigh again before opening the sides or stern.

If you took that route, another thought would be to leave a strip of the floor between the section you have cut out, and a cut in the bow. This would leave you a reference when putting it back together.