There is approximately .9" + or - difference between a 200 and a 180 in overall width. Most 180 tires are recommended for a 5.0-5.5" wide wheel. 200's are recommended for a 6.0-6.25" wheel. I'm no fitment expert, but that could be a problem. Probably should consult the tire manufacturer to see if it would work on the rims width you have on the bike.
I seriously doubt that < 1/2" on either side of centerline on the tire would make a huge difference in wear patterns, or handling characteristics in turns. Some, but not significant.
Most tires on bikes wear in the center more than anywhere else, though the newer multiple compound tires are somewhat better in that respect, regardless of size. Assuming that the tire stays properly inflated (42psi loaded, for the Convertible).
When you say the bike has to be
leaned hard to make it turn once the tire starts wearing flatter, do you mean that more force has to be applied to the handlebar in countersteering, or that her body has to be leaned over further to make the bike turn? Body lean should never be what initiates a turn, so I assume you mean the latter.

Whatever the case, I don't see a 200 to 180 making much of a difference in handling. Just ride more curvy roads...
