Using IK to make hand stay in position?

Hi,

I want my character to have their hand on their shoulder as though they’re holding onto a strap. I’m trying to add this onto existing walking/standing/crouching animations. Right now I’m using two bone IK to brute force my bones into a certain position. This works well enough for the idle pose. But when walking the arm twitches constantly. And when running it completely freaks out.

Here’s a gif to demonstrate. It’s hard to see the twitching on the walk cycle but the running issue is clear. Is my method wrong for this? Would an additive animation approach be better?