My 07 fxstc did not handle like my 99 dyna until i changed out the stock dunlops for avon cobra/venom tires and changed out the stock shocks to progressive 422s and drop in springs. Now my softail is every bit as good as my dyna in the twisties.
I tell you when I swtiched to Avons from Dunlops it was like having another bike, handles well now. I have a 200 rear and it handles as well as a skinny tire softy
I'd check with the tire manufacturer-whether that 180 will work on a 6" rim.
Why wouldn't it?
200mm = 7.87"
180mm = 7.08"
Going wider than 200 on a 6" rim would have problems, going narrower should not.
If anything, when you go to the 180 from the 200 you might want to step up the aspect ratio from 55 to 60 to maintain the same ground clearance and steering/handling geometry; as the 180/55 will be a smaller diameter tire than a 200/55.