I wonder if the water running by the hull creates lift and pushes/pulls the boat forward???
That would be awesome if it were possible. Would that I could just point my bow into the current and the keel would generate lift and drive the boat forward! Don't forget that lift typically pushes boats sideways
What sort of ground tackle have you got? What scope? If there's a lot of tension on a nylon rode, the rode might stretch and then spring back if the current is not constant. I experience this pretty frequently when anchoring, though I have not had the misfortune of snagging my keel on the rode.
Are you downstream of another anchored boat? As the upstream boat swings it will throw little vortices off its submerged foils. When these foils hit your boat, the current might briefly drop in strength, allowing you to spring forward. Alternatively there could be some underwater object upstream similarly disturbing the flow.
What scope are you at? If there's a current pushing you back, it seems unlikely that you could spring all the way to your anchor with sufficient scope.
Finally, if "upwind" an "upstream" are more than 90° apart, it could
be that your boat is sailing upwind against the current under her own windage.
When you're moving forward, is it directly upstream, or at an angle to the current? If directly, I would blame the rode for acting like a spring; if at an angle, I would blame wind-vs.-current.