First, an air handler is just a hydronic coil and ductwork that has the water coming from any source of cold/hot.
As humidity is not a big thing during your summers, taking the cool water from the well, through an "air handler", which may not need any ductwork BTW, and dumping it right back into the well may work for you provided the well can absorb the extra heat. That water can be filtered and used for other things, I suspect, if you wished and not dumped back in.
As nice as the green roof may be, I'll bet a white one will allow less heat gain. I still think doubling or tripling the insulation is a good idea. It is pretty cheap although all it does is slow down the increase in temps in the house, it allows the cooling to keep up with the load better.
I live in a brick house (12" thick) and when I insulated on the outside, the cooling load decreased. In my mind, masonry is superior to wood and insulation which is the predominant construction in N.A. With no other insulation, my house has the same or less heating costs than the wood frame construction. Adobe houses in VERY HOT Arizona can have quite comfortable indoor temps with the wall absorbing the heat in the day and giving it to the cool night at night.
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