Forgive me if I have lost the plot; I expect that many others are in a similar position.
However, to answer the question: “if asymmetric thrust straight flying is possible with zero slip – in that this condition would give you min drag”.
Surely, min drag will depend on the control surface positions required to give zero slip. Control surface deflections may give large increases in drag. In some aircraft, the resultant drag leads to a compromise of allowing some slip to minimise the value of total drag, seeking a minimum. A practical example (although not directly slip / drag related) was for the BAe 146 where asymmetric climbs are flown wings level (for ease of flight handling) and the small increase in roll spoiler / aileron drag is accepted; the large fin and effective rudder provides good lateral / directional control, but with slip.
Thus the solution sought depends entirely on the aircraft type; – the application of the preceding theory.