Ok, so here is my GUESS. I think that your cutlass bearing housing, is leaking around it's perimeter, where it exits the hull. If it were mine, and after reviewing the other suggestions, and ideas, and it still seemed plausible, I would haul the boat, pull the shaft (into the boat), make an airtight plug and insert it into the stuffing box inside. I would get some butyl tape, and tape an area off completely surrounding the cutlass bearing area 2-3' cover with poly so you have an airtight bag, and insert a vacuum source. check and halt any air leaks. Now look for water being pulled OUT of the hull. My 2 cents thinks its going to be leaking on the outer perimeter of the cutlass bearing. For a good vacuum source, go to your local refrigerator repairman, and ask him for a refrigerator compressor. These will draw a nice vacuum to about -25psi. Do not think you can use your own, by cutting it out of your old fridge, Let a professional empty and dispose of the refrigerant. Good luck.
Say you are right and this is the problem, how severe is it? I just had the boat hauled last month and put back in before the spring rush, bottom cleaned and painted, also besides all the regular maintenance, I got hit with rigging failure and am spending mucho dinero replacing all of that. To be 100% honest I do not have any money left as I just spent over $10k last month on repairs to the boat. To spend another $1500 to $2000 to haul the boat, plus not to mention just about every single hauler is slammed busy putting boats in and does not have room until June to take boats out, is not something I am anxious to do.
I am not the type of person to let problems go so this is absolutely killing me and I know boats cost money so I am not trying to cheap out by saying I am too cheap or lazy to have it hauled. I am just trying to think of any other way to find out 100% what the problem is before I haul it or take action.