The 62 grain Fusion is the pick of the litter in OP's list for smaller whitetail.
Our south Mississippi coastal whitetails are similar. While I usually hunt with more powerful rifles (.270-.280-to-'06 class), and at longer distances, I have taken deer inside 150 yards (my max limit with a 5.56 AR) with Barnes 62 TSX. This is an all copper monolithic hollow point design originally developed for larger caliber hunting rifles, like I normally use. Its been popular in big game circles for decades.
In the 62 grain TSX it behaves like its bigger siblings: Rapid expansion to 2x caliber, with 2x or greater permanent wound channel, breaks through bone, and leaves an exit wound with good blood trail. Recovered bullets (rare) have almost 100 percent retained weight.
I've learned to purposefully take shoulder shots, if offered, rather than just behind. Not only does it break the shoulder, causing the deer to drop on the spot, but it expands like a soft point, disrupts heart and lung and leaves a large exit wound.
The 62 Fusion relies on bonding of the lead core to the jacket, like Trophy Bonded Bear Claw bullets. It works. But, the TSX can't shed its jacket, as it is solid copper.