Military bedding for the No.4 involved the barrel pressing down on the forend just behind the muzzle with a pressure of 2-4 lbs IIRC. The muzzle should move slightly side to side when pushed and return to center. Grasp the tip of the forend in your hand and push up on the barrel with your thumb. Use a spring scale to check the resistance.

Tighten the butt stock screw, and the large trigger guard screw. The rifle was zeroed at the factory. The stock is probably shrunk from 40 years without oil. Raw Linseed oil is the original and best finish.

You could take the woodwork off and brush it down with RLO repeatedly over a few days, then wipe down and let dry before reassembling. Best to try that before modifying the woodwork at all.