Use very little roll input in close, since the probe is off center line, you are changing the probes path to the drogue with a roll input. If you need lateral adjustment, a slight boot of rudder is better than rolling. Also relax, by tensing up, you're transferring that tension to the stick and throttle and losing the small inputs you wanted. Wiggling your toes tends to help fight the tension. As everyone else has said, practice, practice, practice. However, don't over do it, set up a mission where you're in trail and try to connect a few times. If you fail, fly away and do something else. Repeat.
Also watch out for the wake turbulence, come in slightly low of the wings and stay there once connected.
I personally do not use autopilot, nor do I have any curves in the stick axis.