I dont have HVAC specific advice for you, but I've lived in a well isolated house in a hot environment (42C max temperatures) and what we did was open basement windows and atic windows, and have a fan point out of the attic window. This created a draft that exhausted the hottest air in the house out, and while upstairs was always hotter than downstairs, it was much more bearable than without.
I imagine a similar setup would help you get the cooler air from downstairs up, and a big advantage is that you can try it with very little cost and commitment.
I don't know how your house is configured, it might not be a solution for you. We have a pretty habitable attic, not those insulation filled dens I see in American houses, so it was pretty easy to try it for us.
Also, we opened and closed the windows every day, we didn't leave it open overnight.