In the northern hemisphere, when turning from a northerly heading, a magnetic compass will lag behind the turn (or even initially start to turn in the opposite direction). It would be difficult to effectively use that that information to maintain wings-level flight.
In turning from a southerly heading, on the other hand, the compass will lead the turn - exaggerating the amount you've turned. Since you are trying to avoid turns altogether, lead is not at all bad. You just need to respond with appropriate restraint to avoid excessive roll oscillations.
On an easterly or westerly heading, the acceleration error swings the compass toward the north as you speed up and toward the south when you slow down.. To the degree you only look at the compass when you are flying straight and level, it works fine. But as things start to go haywire, speed corrections are going to play havoc with your ability to keep the wings level.
In between headings present an amalgamation of these errors.
So if all you have is a magnetic compass, airspeed indicator and ball (or yaw string)... head south. That's what I was taught. I admit, I haven't practiced this teaching, or (fortunately) had the need to implement it, but it seems to make sense anyway.
This assumes that you are not trying to navigate to some specific heading. Whether you roll out on the right heading or not is not the issue. In this case you're just trying to maintain a heading to keep the wings level (and attached) until you get back into VMC. Other options are a benign spiral or induced spin.
Mike Koerner