Hi AoCnG,
I hike the Batona Trail end to end about 8 times a year. Everybody has a different tolerance level for exposing themselves to ticks and chiggers. I have had Lyme Disease and I have also been covered from the waist down with chigger bites a few times, so my tolerance is pretty low. LOL My best advice would be to wait until we have a hard frost. That will kill off the chiggers and cause the ticks to go dormant. The ticks will become active again if the temperature starts to rise above 50, maybe even a little lower than that, but what few ticks I have gotten on me in the winter have always been the larger dog ticks, which are easy to spot. And in all my time on the Batona Trail (from Nov-Mar) I've only had one tick that actually managed to attach itself to my skin.
Another bit of advice I would give you is to keep an eye on the pink blazes. There are a lot of fire lines and dirt roads that cross the Batona Trail and it is very easy for somebody who is not familiar with the area to be daydreaming or admiring the scenery and walk right off the trail. If you go 1/4 mile and don't see a pink blaze, it's probably time to backtrack.
As far as pictures go, from about mid-October to the latter part of November, you can find some areas from Batsto north on the Batona Trail to Lower Forge where the ground cover has turned a beautiful shade of red. Right now you can get some nice shots of areas that are completely covered in ferns near Apple Pie Fire Tower. That area is accessible by dirt road so you don't have to worry about ticks & chiggers (so long as you avoid the tall grass) In fact, if you hike along the dirt roads in the pine barrens this time of year, you're likely to encounter snakes, frogs, lizards, and various flowering plants.
Good luck!