I very recently got my old 416 back
The swivel plate on yours and mine is held to the stock with a wood screw to the rear and a machine screw to the front.
The torque of the wood screw is 'dont strip the wood'.
The front screw is a different critter. It goes up into that barrel band and tensions the front end down. The other screws on way back around the trigger guard and magazine do Not hold the barreled action in the stock. The rear barrel mounting screw is forward of the magazine, into the forearm handhold area. This means it is the barrel held to the stock and the action 'floats'
I snug up that rear barrel screw well (but remember, it aint a headbolt on a Chevy) and have today played around with the front band (and swivel plate) screw tension.
My best results were with that screw only to fullfill the take-up and lightly contact its recess in the plate. No Tension...and it will not stay there. Im considering a light dab of light-duty Loctite to just give me some purchase within those threads so it stays where set. I am reluctant to not have any screw, as in a free-floated barrel, because of that one only, well up rear screw.
Btw, this no tension setting is consistent with what had generally been found by others of knowledge and experience on other rifles with front tension assemblies.
If you want to mess about with that front screw be aware that you want to make adjustments with the rifle in a horizontal position, as in shooting, with nothing but the barrel weight settling it down.
Also be aware that because of this design you may be loading the forestock with your sling and affecting the group location (poi) and size.