Ok... okokokay... check it out...

You need:

Two ultralight train axels with the usual feynman bevel.

At the center the rear one is a kind of cradle in the center with a gearbox. It goes on top. The tire rests atop this thing and its job is to transfer the torque from the tire to the axle. You get the idea! Compensating for the size of the train wheels, rotating the rear tire with your legs in the usual way should feel just like it does when you're riding on level asphalt (standard asphalt. at sea level.)

The front axle just has a cradle to strap your front tire to.

NOW the only thing you need to do is:

With bike mounted, ensure the distance between the axles doesn't vary (the bike itself might be sufficient for this, or mostly sufficient). Ensure that the axles stay parallel to each other and are normal to the centerline.

This is a bunch of cables and maybe a carbon fiber rod. It strikes me as very foldable too. Wheels pop off and it goes in a 8x16xN box (where N is your desired gauge expressed in inches.) Like a trombone case.

Imagine a 3" tick-walled carbon tube for the axles. Totally sufficient; dozens of grams or whatever.

Extrapolate. Apply more carbon fiber. Wheels? We got wheels! Cheap, mass-produced wheels. We can just pick the ultra-ultralight ones and apply the feynman bevel

It's no more stupid than a collapsable canoe.

[Update] It may be a chomemoly pipe dream but I feel like if you had four very tight cables going from a single point on the upper nut-buster bar on the bike to a point on the axles just inboard of the train wheels, you'd be ...done? If the front and rear tires are firmly secured, it sure seems like it! Somehow need to not allow for the front tire to rotate, or just attach directly to forks.