My uncle had a similar problem with his 30-06. Handle was loose when he got it, also trigger pull was incredibly stiff with lots of creep and overtravel after the break. Took my allen set over to his house and tightened up the rear Bolt Screw and adjusted the trigger (his has a 3-screw trigger) and it was like a whole new rifle.
I will bet if you tighten up the screw the handle will loose the play it has now.
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