The "rotation of the entire vehicle" part was because the scenario, currently, is:
1. Use aerodynamic lift and grid fins to aim to the side of the barge.
2. Start the engine.
3. Re-aim to the middle of the barge.
They do this since they still fear that a relight might fail and the heavy octaweb structure will punch a hole through the barge. It may well be that the next landing will be aimed at the bulls eye already during the final, unpowered part of the descent.
I doubt this can be done without extra thrusters for fine control over velocity and position.
It can be. We've already seen it done. The difference between success and failure in this most recent case has been very slight. It doesn't take any major redesign to fix that sort of a thing. Get real.