I grabbed a range finder to begin this process, but it turned out to be a split image type intended for golf.

The golf ones don't do the job, as you found out.

Does the angle cause much distortion?

Angle will make a difference to the measurement but it's not generally great enough to cause a miss. With the calibres being used almost any impact will cause a problem for the target. Center mass is the way to go and if the range is off slightly it'll still hit something soft. You know?

with a laser range finder, does angle on the painted surface reduce the accuracy by bouncing

This is a good question. Yes is probably the answer, but again, probably not greatly enough to affect the overall shot. When I range out culling I'm lasing fury animals which are non reflective and if the range is off a little it rarely makes a difference. I'd say it's no factor, minimal enough to not affect the end result significantly.