Ahh, smell that? Rarefied air, friends.

Also, I think my final result puts me firmly in the 'messy thinker' camp.

I don't think that if I just started with Level 10 that I would have solved it. All of the tricks and intuitions you build up through the previous 9 levels aid greatly in figuring out the more difficult levels. Such as, looking for vertices that are obviously out of place and should be grouped with their neighbors or that moving lesser connected vertices (2 or 3) to the edges will give you more space to work with. I found levels 9 and 10 a cakewalk because level 8 took me almost a half-hour. Waiting for a furniture delivery, I had plenty of time.