The board on the beach was not a good example, I grant you that.
Lift does come from two opposing forces and the boards momentum is one force when combined with the air under it, provides lift. Once the momentum drops, so does the lift and board.
The fin, converts lateral resistance to forward momentum as you say, which in turn allows the wetted surface to be reduced as the speed increases, which increases the apparent wind under much of the board. I really don't know how much lift if any is happening here, but it seems that there has to be some.
Wide boards with big fins tend to tail walk or take off more quickly than narrower boards with smaller fins. The difference is speed. They all will tail walk or take off at some point. When a fin is too large for the speed and board, it wants to "lift" to the surface, after all it is a foil. This in turn causes the board to become unstable and tail walk, which I assume is a result of air passing under the board and the fin trying to raise to the surface. If the fin always remained perfectly vertical, there probably wouldn't be much instability, but that is not the case in choppy water. Your example of towing a board with or without a fin is only valid if the fin remains perfectly stable and vertical, which would probably never happen.
I know we are going around in circles here, but nevertheless, I have enjoyed the discussion and am always eager to learn and or debate and issue.
Formula 160; iSonic 111; HiFly Move 105; Tiga 263; '85 Mistral Superlight.
Maui Sails TR 11.0; 9.2; 8.4; 7.6; 6.6; Maui Sails Switch 6.0; 5.2; Maui Sails Global 4.5; 4.0.