Current home air conditioning units have an air handler inside the house which blows air through a radiator. The radiator had cool refrigerant which cycles to an outdoor compressor unit. The bottom of a standard indoor air handler is built with a plenum to catch and drain condensation. This is then plumbed outside.
Dehumidifaction should not be a problem.
I'm thinking cannibalizing an indoor and outdoor unit. These would have refrigerant in the guts which would need addressed. Used units can be had for cheap-I know an AC guy, he replaces old and busted units regularly. A new unit could be ordered without refrigerant, perhaps for a surcharge, but this would be a purchase on the order of $5-8K. These would come with everything. Coils, valves, blower, standard duct outlets, all the bells and whistles.
I'm no where near ready for this investment. Solar PV is higher on the list. Paying for this place is above that.
Looking at different potential parts may also be needed. The AC/refrigerant systems operate with the refrigerant in gas and liquid. Some of the plumbing gets pretty small in there. Also, the water is kinda hard. Running it through a new device designed for something else is not exactly the best idea. Scale buildup can stop the thing dead, there goes my time, effort and hard earned money. If I'm going to come up with a freaky simple idea, it really needs to work to keep me out of the lunatic fringe.
Auto/truck radiators are designed to handle water as the internal conductive fluid in conjunction with blown air. Its the same sort of jig, coils with fins, and don't have environmentally incorrect refrigerant residues. Antifreeze will rinse off real easy in my brothers driveway when he's at work.

Fittings can be fabricated fairly easily. The things can handle the pressures and temperatures involved. There are a couple of junkyards in town. If need be, I could build the system with multiple radiators. A drip pan is easy enough to build, even with a drain fitting.
I'm thinking if I were to build an experimental model, the garage would be the place. I can screw it up but good to get the details and bugs worked out before I put one in the house.
My objective is to use the water which would already be flowing as a heat source/sink to heat/cool a space with no significant additional energy consumption. Caveat: gotta use a fan.
What I need here is for you good people to rip the idea to shreds.