Ron:The term starter "drag" is something my generation grew up hearing. I imagine that started when the bushings in the starters became worn, and the armature would "drag", or rub, in the field coil pole shoes. This grounded out the magnetic field from the coils and the starter would turn very slowly. I doubt if this is what you have. The starter could not be failing to disengage for "a couple of minutes" many times, the drive would be destroyed. It would produce a whirring sound, not a knock. The noise you hear may be engine bearings, knocking until they receive a good oil supply under pressure, or loose pistons, which get quieter when the warm up and expand. Blowby, causing oil to drip from the breather, would also indicate worn pistons. Without hearing the noise, I can only make these guesses as to what they are.
John