I see that the bilge water is intended to be pumped into the cockpit back by the scuppers.
No, it's not. The bilge pump outlet is on the starboard side of the stern, a bit less than half-way up.
I get water from various leaks I'm always running down, as well as some coolant from the FWC system.
Are you talking about coolant from the closed-loop part of the heat exchanger that circulates thru the engine? If that stuff has anti-freeze in it, you're not supposed to be putting that over the side, anyway. And why is it leaking?
I'm thinking about putting a thru-hull out the stern, akin to the raw water out from the engine.
I guess we now know why the OP removed the manual bilge pump.
Very strange, the things some boat owners do.