I vote Shawnee in November. Don't know my schedule yet, MAY be changing employers (Interview in just over an hour) so will wait n see.
Hint about Shawnee: get a hiker's map AND one of the horse rider's maps. Neither show all the trails & there are some rough sections the hikers trail take that the horse ones avoid, & vice versa. Both are decent Topo maps. ALSO, per the rangers: Park at the ranger's station NOT in the hiker parking lot as they have had quite a bit of vandalism in the past. It will add about 1/2 mile each way to your hike, but when there last time, a truck had both side windows busted out.
I agree with the previous posts, Shawnee is a bit (a LOT?) rougher hiking compared to "Z" but has the benefit of natural water along the way. Or at least did last time I was there.