[JonPR]

When strumming you shouldn't be anchoring at all, normally. The movement should come from the elbow, swinging the forearm, usually with an additional flick of the wrist. The hand can be open or closed, but it never normally touches the guitar.
Anchoring the hand - either resting the wrist on the bridge, or pinky on the scratchplate - is for more intricate rhythms, or for picking arpeggios, or other fingerstyle techniques: anything where specific strings need to be hit at specific times, rather than all of them at once.

It's hard to see how the problem could simply be caused by the difference between an open and closed hand, unless you've changed your position in some way. If you're playing intricate picking patterns which require anchoring, then it's quite likely that if you're anchoring by resting the wrist on the bridge (instead of pinky on scratchplate), that changes the balance of the arm, and perhaps you've introduced additional tension into your arm and shoulder, as you try to control it. E.g., the forearm and wrist are now fixed in place, in a way they're not if the pinky is the anchor.