I suggest doing one of the following tweaks to Limb IK, depending on what more you do with your puppet.
Tweak Limb IK's "Elbow Flip Threshold" until you get a good result. The default is tuned for front-facing characters. You will need to animate this value too if your puppet can face different directions.
Set Limb IK's "Apply to" option to "Legs" only - this will disable IK on arms and make the puppet fully respect the elbow positioning from Motion Library. This is probably the best if you only use Motion Library. The downside is animating with draggers at wrists will now bend arms unpredictably and stretch arms infinitely.
Take full control over the bend direction by unchecking "Auto Arm Bend" and checking "Reverse Arm Bend Left/Right" as needed. This guarantees fixed bend directions while losing the bend direction transitions.