Back to the original issue, the cracked floor.
This is an important structural component. Not only does it support the mast and transmits the weight of the mast and the rigging tension into the hull structure, it also serves to keep the two sides of the hull apart. Supporting the cabin sole is the least important function, although still an important function because the sole helps to stiffen the boat and keeps the hull from twisting.
From the photos, this floor can not be repaired, it must be replaced. The mast needs to come out. It will only be in the way and any effort to shore it up while on the boat will only add stress to the hull possibly distorting some of the hull. But mostly because it will be in the way.
All of the other floors should be evaluated. Pearson, like many builders back in the day, used wood as the core and encapsulated it with glass and then drilled a limber hole and didn't seal the exposed wood in the core. This provides good access for water to get into the core and cause rot.
The old floor must be cut out and a new floor installed. All the other floors should be carefully inspected for damage and rotted cores. The strength of the floors is not in the core, it is in the skin, so the core material is not all that important. Foam, solid wood, or plywood all work as core materials provided the external glass layer is sufficiently strong and thick. The core provides some strength by keeping the sides of the box from bowing inward, but that is about it.
Repairing this is a major structural repair, not to be taken lightly. Consult some well researched sources, such as the West System manuals and Guogeon Brothers on Boat Building, for more advice. Andy on Boatworks Today may have additional information on structural repairs, especially on the videos about the Bertram repair.
Good Luck!
