Otter, a couple of related ideas have surfaced in the past.
It is possible to replace the crank arms with an older version that is solid aluminum and threaded for bicycle pedals. You can install clip pedals and wear your cycling shoes!
Someone else mentioned fashioning slings to the pedals to support the heels -- don't remember if this was ever built it or not.
I wedge my feet in the straps -- that seems to keep them attached and supported pretty well. Not a perfect solution, but it helps!
If you give it a try, be sure to let us know how it works out!
