A good pair or road wheels will cost you at least twice that much, and for quality, you'll spend more. So, spending $250 to replace wheels that are already doing what you need is a waste.

A road bike is a wonderful thing, hills or no. But if you have 40 lbs in a pannier, you won't get much of the benefits it has to offer. I don't know what kind of bike you have now, but the gearing on a road bike might not be appropriate to climbing with heavy cargo.