Sorry, I don't have time to read this entire thing now. But from engineering standpoint.

The Trail (distance from where line through the steering bearings, to the contact patch (which is directly under front axle) determines the dynamic restoring force.
This is the force trying to straighten the front wheel due to forward motion.

The distance of the front axle in front of the line through the steering bearings is a lever arm, the angle of the steering bearings and that lever arm determine how much the frame is lifted by turning the handlebars. That is the static restoring force. It is proportional to the weight on the front tire too.

To make this short. you must have hit a pothole and bent the front fork. Even a tiny 1/8" bend will change both of these.

Moving the axle back by 1/8" lessens the static restoring force. Now the bike seems less stable at low speeds.
Moving the axle back by 1/8" lengthens the trail and increases the dynamic restoring force. Now the bike is harder to steer at higher speeds
.
Your muscles have been trained to expect a consistent behavior from the bike, and now they are messed up by inconsistent and opposite changes to the restoring force a different speeds.
If it was consistent it would not be so bothersome, but I think it is the relation of the low speed behavior to the high speed behavior that is messing with you.
Even if the front fork does not seem bent, I suspect you want to bend it back so the front axle is farther out front.