So sorry to hear about your loss of animals. I would urge you reevaluate your ammo and your shot placement before you condemn all handguns as the issue. As far as shot placement goes I would recommend either center shoulder, breaking bone if you want to quickly anchor a deer sized animal. For ammo I recommend a heavier JHP that will penetrate fully with some expansion. I have killed many deer with XTP bullets in 44magnum. I have killed a Whitetail and a red sheep with a 460 using 240 XTP Mag bullets. Both quick kills with full penetration. I am not a fan of the pointed FTX bullets. They are fairly light for their diameter and they must expand to create a wound channel. If I had to use them I would experiment with pulling the plastic top and shoot them as a hollow point.
Regardless of rifle or handgun you need bullet placement in the vitals and a good wound channel to secure a kill. Many deer run off to be lost with rifles too.