I was actually thinking that the way you clean tires is to turn the engine at about a 45-degree angle from upside down with power applied to the drive -- this keeping any of the solution from falling down into the mechanism or being thrown where it might get in your eye. There are a variety of ways to get power; a 'cheat' I used was a short length of power-feeder track on the tender pickup wheels attached with a Velcro strap around the tender body.
Yes, tortillions are superior to both Q-tips (less lint and better scurf pickup) and foam electronics-cleaning swabs (more 'tooth'). I used them with solvents and solutions, though, following up with a couple of passes with the demineralized water on a separate one.
(As an aside, some tortillions are made so they can be sharpened in a pencil sharpener...)