He said nothing is mentioned in the OM, I am just pointing out that it does say in general replace as a pair.
A tire with 9k miles on it will definitely have the tread worn more than a new tire, and that's going to cause an imbalance - How much of an imbalance will depend on the amount of wear.
The owner's manual does say "It is recommended that the two front tires or two rear tires
generally be replaced as a pair. "
If it were me, I'd probably replace both rears (at least) to avoid an imbalance.
It depends on how bad it is, but if you want to clean the seat very thoroughly you could take the seat out, take it apart, take the seat covers off and clean the foam padding, seat frame and the covers. This would be a lot of work and probably not worth the effort unless you can't live with the...
This probably won't convince geep81 these tires are worth a damn in the snow, but PA4s are 3PMSF-branded, which means they meet certain criteria for winter performance to be considered severe snow service-rated.
No one is arguing that Blizzak WS90s or Micheline X-Ice aren't great tires - they are extraordinarily good in snow and ice conditions, but you do give up some of the wet/dry handling performance. If you're mostly going to drive on snow and ice they are definitely the tire you want for winter, in...
Since you're looking for science, how about some testing by Tire Rack?
Tire Rack Testing Performance Winter / Snow Tires
Tire Rack tested the Bridgestone Blizzak LM-60, Dunlop SP Winter Sport 4D, Michelin Pilot Alpin PA4, and Pirelli Winter Sottozero 3.
Tire Rack test video
Tire Ratings Chart