Keith,
You may have confused me here.
If the forces are in equilibrium, then the ball reverts to a simple pendulous indicator giving us some measure of the net force vector direction ... in the bank-into-the-live-engine scenario, the ball will slide toward the lower wing .. as we expect in the normal OEI climb out with wing down.
As I see it, it is a simple exercise ...
(a) after the initial failure dynamics are sorted out, in the wings level, constant heading case there is a remaining lateral fin force toward the dead engine resulting in a small lateral acceleration which is, in turn, shortly balanced by a opposing lateral fuselage force. The end result is a modest steady velocity toward the dead engine resulting in a small sideslip.
(b) to get rid of the undesired sideslip, one needs to generate a lateral motion toward the operating engine while maintaining heading... the only practical way to do this is to bank sufficiently toward the live engine to develop a sideslip sufficient to "cancel" the existing sideslip toward the dead engine ... at which stage we end up with nil slip, constant heading and the ball out a bit, typically half a ball, toward the live engine. The actual forces will be complicated by the need to balance the yawing moment due to the fin/lift vector couple.
Overall, I think that it is quite misleading to view the ball as a slip indicator as that is not it functional purpose. In normal operations we make inferences regarding the slip situation based on the pendulous indications of the instrument but it still can only give an indication of where the net force vector might be.
Perhaps I could ask you to revisit your post to assist .... ? .. or have I misread it and find myself talking the same tale in misplaced ignorance ?