If you have oil, wouldn't it be a lot cheaper to run an oil water heater? Electricity certainly is the worst way to make a BTU.
I don't know what you pay for oil, but I found a current online price at onlineheatingoil.com of $2.37/gal. With an energy content of 138,690 Btu/gal (40.6kWh) and a low-end efficiency of 85%, that's the equivalent of $0.07/kWh electricity. So for probably only a few hundred dollars up front, you could cut your bill by more than half and pay back in less than a year.
Even without considering things like interest and inflation, your numbers as you stated them don't add up: $80/mo is a 3.6, not a 3 year payback of $3,500 if you assume you can use use the solar heat all the time, which you can't. Now perhaps if the real payback ends up being 5 years it is still worth doing, but I'd really want to know before spending the money.
I don't mean to rain on your parade here, but I don't like seeing people make potentially bad decisions based on overexcitement about environmentalism.