geothermal cooling with no heat pump?
The first problem that the heat pump solves is the small differential between the ambient air temp and the temperature you'd expect to get out of such a system. 

Let's say your home is at 80 degrees. Let's say (with only wild guesses at actual results) that the air that comes off your radiator is cooled to 65 degrees. (You're unlikely to get anywhere near 55 degrees, your water temperature, with a simple fin-contact radiator.) You now have an air temperature differential of 15 degrees. That's not much, and unless you move massive amounts of air it's not going to give the results you're hoping for. You may drop the room five degrees, or even ten, but that ignores the primary benefit of a true air conditioning system: humidity reduction. 

This is the second problem a heat pump solves. By dropping the temperature in the room without a condensation stage, you've now effectively raised the relative humidity. This reduces the sensation of cooling you'll feel, and it could actually cause ugly side effects with respect to your home. Now your windows and walls may start showing condensation because they're cooler than outside, but also wetter. 

Basically, if it was that simple, everyone would do it. Unfortunately, it isn't. I'd upgrade your window units or add another one. For the cost and effort you'll come out ahead. (Don't forget that a well uses electricity, too.)