I found a feasible solution for your project .. Hydraulic Ram Pump..
What you can do is have a tank in your basement then pump the water up another tank in your attic which will then supply water pressure to your house..
To get water up to your attic you use a Hydraulic Ram Pump it uses the water pressure of the water falling water from your down spout to pump water up to the attic. They can be expensive but i found a guide to make a homemade Hydraulic Ram Pump using normal pressure plumbing supplies.
They are not very efficient about 25% so will need will need to make sure you have a good overflow... It can also be rigged up to flow directly from the down spouts to the attic and would be alot more efficient but there would be trapped water to freeze.
You can rig a toilet fill to add well water to your attic tank if your water supply gets to low..
A pump that uses your well water pressure might work too like for basement sump pumps
I Personally don't think its worth the effort and don't think it would ever pay for it self especially with well water.. but it seems like a fun and green project.
Here is homemade Ram pump blueprints
Have to pay for a year subscription for this one
looks better though