Seeing the context of that statement, I might even suggest "meticulous" or "precise" as a possibility for the tidy/neat idea. Your metaphor of the freshly washed white cotton shirt is very vivid and adds to my impression of how Daisuke sees Meryl's skating. How lovely that one of the world's greatest skaters sees Meryl that way!
Unimpeachableness is a perfectly acceptable word according to what I found, though unimpeachability was listed first. That just means that one is preferable, but both are correct.
One of the beauties of translation is that it brings to mind all the range of possible words, and it's like being presented with an array of beautiful fabrics for sewing. Which to use? They're all tantalizing. Often there's more than one good way to translate something, which is why we have so many editions of, say, The Odyssey or Dante's Divine Comedy translated into our respective languages. (In fact, I've read translations into English of The Odyssey in both poetry and prose...the possibilities seem endless.)
I love the list of skaters that Dai mentions. Definitely not surprising that both Lambiel and Buttle are on his list, yes? Both of them have Dai's combination of technical prowess and musical grace that lifts them out of the ranks of mere athletes. I'm fascinated by the fact that he doesn't cite any ice dancing couples. He names one skater from each team but not the other. I'd love to spend an hour or two listening to him talk about what he sees in each of those skaters, wouldn't you? That would be a master class to remember!