Dragged limbs not staying put after recording; everything snaps back to default pose

I searched the forum and found a similar issue from 2018, sounded like a bug back then but I'm not sure if it's still there or I'm doing something wrong.

I'm doing a lot of animated bits for a broadcast job. I have rigged my own puppets and for the most part they are doing the simple things I ask of them (basic body tracking and some walking). I just did a new scene that had two of my puppets sitting down and then toasting with champagne glasses, so all I needed to move were the arms holding the glasses. Their rest pose is standing with arms akimbo and legs straight, so before a take I bend their legs so that they're sitting and put the non-moving arm on an armrest, then hit Record and drag the other arm for the toast. It all works... until I hit stop. As soon as I stop recording all the limbs snap back to the default position. If I play back the limbs go back to the recorded positions but still snap back to default when I pause. Obviously if I disarm the puppet then they stay put, but I need to do several takes and each time I wind up having to reset all the limbs before I start recording.

Am I missing something, or is this by design? And there's probably no way to just keep recording the one Dragger (left wrist) while "freezing" the other limbs in place is there?