[Bicycle Bob]

It is years since I've followed homebuilt aircraft, but I think some guys were getting over 100 MPG at over 100 MPH. The small-bore racers are a good place to start looking. A super-economy ultralight would still be speed-limited, but far less hassle. You might also want to look at powered sailplanes, and ride the thermals and ridge winds for free.
For real economy on long flights, you climb to the thin air using turbocharging and go fast.
One caveat: Only 30% of homebuilt aircraft are flown. 10% by the first builder, 10% by the 2nd, and 10% by the third. They are a lot of work, and you need confidence in the craftsmanship. However, you can choose your favourite material to work in from a broad selection and come out at a competitive weight.