The stated source for the 3365-mile figure was the AASHTO route log, published in 1989. But when one actually looks at that log, one finds that in order to reach the cited 3365-mile figure, one must include not only the milage for mainline US 20, but also the mileages for all of US 20's auxiliary routes (that is, each of the bannered routes with designations like Alternate US 20 and Business US 20). But obviously those auxiliary mileages must be subtracted out in order to arrive at an accurate total for mainline US 20, which according to the route log would have been only 3237 miles.
However, when US 20's mileage was referenced in 2016, the AASHTO route log was at least 27 years old, possibly more. That raised a red flag in my mind, so I checked it out myself and found that the actual mileage is now even less than 3237. Why would the mileage change after 1989? Because during those 30-some intervening years, the route of US 20 has been realigned in several places (perhaps most significantly through Iowa, where it is now a freeway across most of that state). Every time something like that happens, the mileage of US 20 changes. As of 2020, when adding up recent data from each of the states that US 20 passes through, that total is closer to 3220 miles.
So even if we choose to add the cross-country mileage, and we choose the longer route through Yellowstone, we are still 68 miles short of the 3365-mile figure listed on the signs. And one could argue that the mileage through Yellowstone should not be added at all, which then calls into question whether US 20 is actually the longest highway.
The midway-point along US 20 is in Nebraska. The exact location is dependent on how one counts mileage through Yellowstone. Half of 3310 is 1655 miles, so the midpoint of US 20 would be between the towns of Newport and Bassett. If we go with the shorter distance of 3296, that would shift the midpoint 6.9 miles further west, which is essentially right in Bassett.
Additional research: Mike Roberson