An interesting solution, but I probably would have tried a Penske box truck first. I wouldn't entirely trust a U-Haul to make it the full 300 miles without some kind of a mechanical problem, even when the box is empty except for my suitcase and carry-on.

Moving truck rentals are better set-up to do one-way trips than the airport car rentals. Also, you won't get the airport surcharge. Might be a little more expensive than a car rental or the Lyft, but I guess you could always fill up the truck with Chicagoland-specific goods, if you wanted.