In your zone, I would be concerned that chopping them in half would encourage regrowth, and this is not the time of year you want plants putting out tender new growth. I would most likely take a pair of old style hedge pruners and deadhead in a few big whacks, and then wait until it is colder, or even early spring to prune back by half.

I cut mine down last week. This is only my first full season with them after being planted last August, so I also hope it is not too late. I assumed they are like most chrysanthemums which follow the general rule no later than July 4th. They are already showing signs of new growth at the leaf axils. I have read these are very easy to root from cuttings just shoved into the soil (like sedum) but I am running out of room and didn't try this, LOL! I planted this and many other single-flowered mums (the so-called Korean mums) for fall color and especially as a late food source for pollinators.

For a late summer/fall blooming, sun-loving plant like Montauk daisy, it really needs good summer sun, though it wouldn't have to be all day if the rest was bright shade such as along an east-facing building. Many of the spring ephemerals like blood root would do well. Or other plants that complete the majority of their lifecycle before the leaves fill in such as some of the earliest bulbs: crocus, early daffodils, or tall Alliums. Or plants that thrive in shade such as hostas, Solomon's seal/Polygonatum, Actea (AKA Cimicifuga)/bugbane, ferns, ginger/Asarum, etc. Often brightly colored or variegated foliage in a range of textures, size, and shape do well as the main show in areas where the flowers are finished by late spring.

Deer & bunnies don't touch mine (and boy do I have both in abundance). Moving it to a full sun location & trimming will do the trick. Mine need dry soil (heavy clay here). When you trim it in April, stick the cuttings in potting soil; they root easily.