Switched DS4 controllers and the new one has no calibration issues at all right out the bat. Using 5% or less deadzone on the left and right joysticks, and all works great. I'll try and figure out a way to calibrate the other one. Maybe through the Ps4 there is a calibration that it can remember?
Tried doing that multiple times. Ended up being a bad controller actually. Hooked it back to the Ps4, and it was doing the same thing. Googled it, and other than a controller reset, there is no calibration for the Ps4. Threw it away and bought another one at Walmart.
Sorry for the post, when it turned out to be bad hardware.