sub-floor below bulkhead removal

[Morning Wood]

I am restoring a large wooden powerboat and have torn up all the hardwood floor, sub-floor, most cabin sole bearers, most frames, and many floors. I'm saving the bulkheads (walls). I am now looking at my best plan of attack to replace the sub-floor under many bulkheads inside the boat. I have cut the sub-floor back to the sole bearers closest to the bulkheads. How am I going to remove this small portion of sub-floor from under the bulkheads, and run new sub-floor under them without forcing problems upwards (over-jacking).

Just looking for alternate perspectives. Hopefully I'm just being blind to simplicities.

Thanks