Hey Leif,
Well we had a nearly empty rink in Swindon today, so thought I'd have a go at CW crossovers - a bit wobbly, but slowly getting there. As you say, a lot of people can skate well in one direction, but it's a different kettle of fish going the other way around. Sorts the skaters out from the wannabees (I am firmly in the latter camp at the moment).
I'm wearing hockey skates for LTS, the 3-turns are doable, but a greater degree of skill is required than that which I currently possess. Practice, practice, practice (or, as I prefer, your mud analogy!). As for spins, I find if I get the blades absolutely flat, I can find a sweet spot that is potentially able to spin, but the margin for error is much less than that on figure skates.