The keel on your 34 is filled with either foam or a mix of low quality cement and river gravel. A 75 would most likely be cement and gravel. If there's so much water in there that you feel you need a drain plug - you've got a leaking aft coupling, or a badly corroded shaft log.
The only other cause is severe damage to the bottom of the keel, the kind caused by multiple groundings and amateur repairs.
The most common cause is the two studs that hold the aft coupling to the hull corroding and weakening. Shaft logs do go bad on these boats, usually right next to the stuffing box coupling where oxygen is low.
The bilge on your boat is a false one - it's a thin layer of fiberglass that the yard laid over the keel after the ballast was poured when the two halves of the hull were joined together. If water is slowly seeping in under the engine, or in the bilge just under the main hatch in the salon, it needs to be addressed.
Does the water starts seeping in from 30 seconds to a few minutes after spring launch? That's a telltale sign.
It is fixable for one to three boat units - depending on how bad the damage is. Better to fix this now, before the wobbling shaft does more damage.
Best of Luck!
If you want to try this yourself I have all the pictures of what it looks like torn apart. You'll need a prop and shaft puller and good alignment skills.
Besides its another hole in the hull!
