Sounds like you need some vise pads to hold your stave without much pressure. You don't have to clamp the splice in the vise, you can clamp the fade area.
I use these, easy to make, easy on and off.
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I highly recommend a post to support your stave while you work, this will minimize the pressure you put on a stave while it is in the vise. This is an old picture with cheap magnet vise pads, they worked poorly.
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Another thing, the glued area of your splice is a lot stronger than bare wood, it is highly unlikely vise pressure will harm it.