Hunter diagram
According to my Hunter 28.5 manual, the plumbing drawing shows a flexible drain hose leading from the ice box into the primary bilge area (where the pump is). That, of course, does not make it so. If it is so, then maybe the hose is broken underneath the sole. Short of taking up the sole to see what's what, you might just try something simple like a length of rubber hose that you can cock with some sort of valve and just manually drop the hose end into the bilge when you need to drain the box. You could stow the hose under the sink, or under the stove.I have not used my ice box since buying this old boat last year. I would not be shocked to find I have the same problem. I do share your problem with the aft ribs of the bilge...water that collects there (in my case I have a fresh water galley piping leak in that area) takes for frigging ever to seep into the bilge. Very very annoying. I keep a very small wet/dry vac aboard to suckup water that collects there.Next off season I am going to replace my sole for reasons unrelated to this issue. I am very curious about what I am going to find under there. And if I can improve the flow of water to the bilge sump, you can bet your booties I will.Do you know if your head shower "sump" drains directly into the bilge sump or does it flow into the aft bilge areas? The plumbing diagram shows a similar flexible tube running from the head floor to the bilge sump.