@lewm, you are right that the linear speed of the record by the stylus which decreases as the arm gets towards the center of the record does not change friction. Thus if you had a blank record the friction would be the same anywhere on it.
Although it is termed as friction, as groove velocity increases more energy is required to keep the stylus moving. The stylus has to be accelerated harder which would increase the force the groove places on the stylus which would increase friction. This happens momentarily as the stylus is forced to change direction but the additive effect is to increase friction.
Overhang has almost nothing to do with skating unless you play the label area. It is almost purely the result of a pivoted arm having an offset angle. Decrease the offset angle and the skating force decreases. A straight arm has no skating. There is a relationship between tonearm length, offset angle and overhang but an offset arm will skate even if the overhang is zero. Try it millercarbon. Set your tonearm so there is no overhang and play a blank disc with your anti skating defeated and watch what happens.