All joking aside, that redneck trailer E-dolly by using a 1/2" drill as a friction drive is brilliant. It would not be difficult to to make an adapter mount that clamps onto the front landing gear, and is easily removable before takeoff, or for airworthiness inspection. If you feared that you might forget and then take off with it on the nosewheel, you could attach two limit switches and two RF senders, coupled with two LEDs in the cockpit that flash red the entire time the drive is mounted. This would also help you to remember to remove it after parking, to prevent theft.
Why two? if its not important, you don't need any, if its important, you need two independent parts because its aircraft. Raising a retractable nosewheel with the friction-drive on it may not cause a crash, but any damage to the aircraft skin can be expensive to fix well enough to maintain airworthiness, as sheetmetal cracks can spread rapidly from the vibration, and MUST be fixed in a timely manner.
Since the dolly thats shown in the second post is several thousand dollars, its not crazy to spend a couple hundred on a quality 24V/36V cordless drill. The drill doesn't have to be ruined by the adaptation, you could make a friction-drive out of it that can still be used as a cordless drill...drills can also be found with a short snout and a 90-degree head.
Also consider making the roller a separate piece that is belt-driven, and that would open up a wide range of performance and speed options. The roller could be covered with truck brush-on bedliner with very coarse sand mixed in.
I make friction drive rollers with one-way clutch bearings in them for $40. The roller stays in contact with the tire at all times with almost no drag at all, and when the motor is engaged, the moving-frame drive is pulled into the tread deeper to increase traction (designed by EVTodd).
If someone decided they wanted to make a DIY dolly similar to the production unit in the second post. A brushed motor and controller from TNC-scooters are very appropriate due to low miles anticipated. And rather than independently battery-operated, they can be corded to the planes battery via a socket in the aircraft skin under the engine. The controller could also be corded...piece of cake to design.