How big was "all over the map" in group-size terms? If you bullets are truly tumbling, and you are shooting at 100 yds, you will not hit any reasonably sized backer consistently. A true tumble will give you a nice side-type profile of the bullet. It is typically not subtle.

It is relatively easy to mistake paper tearing weird on a bad backer for a tumble.

Two thoughts:
1) Not a good idea to start at 150gr, odds are it won't work out well. Especially with a light bullet.
2) 1:32 twist may be too slow. If this is the 200gr Shockwave or a similar .40cal bullet, they are long for caliber and it is possible that you need a 1:28" to stabilize them.

FWIW I had hunted for years with the 200SW at 110gr Triple Seven. And I've shot deer and ranges you probably wouldn't even think about just fine. It's all about knowing where the bullet will hit at the given range, not about a few inches of drop making a huge difference. Accuracy trumps trajectory.