You say it feels loose. In the action? The barrel sounds like it floated. Solid to about 2" of the recoil lug. That's about what I do but, where the barrel does make contact, is the contact point square across the barrel channel? Needs to be! Thats important. If it's feeling loose in the action, could be that cleaning solvent over the years has soften the wood around the bedding points. In that case, you'd need to take out the soft wood and re-bed, I like micro bed but others probally work as well. At the same time, I'd do the recoil lug. Cut away behind it and refill. Be sure and put several layers of tape on both sides the front and the bottom of the recoil lug. You don't want the recoil lug mortise to grab the lug, bearing on the back only. Make sure everything that the bedding compound MIGHT touch has a good coat of release agent and tape all around the trigger housing or take it off the action. Use a shim to hold up the front of the barrel and keep it from falling and lifting the rear tang. Easiest way is to put some clay, just a bit, in at the forend and re-install the barrelled action to pull the front of the barrel down into the clay. Play dough works well. Plug the rear tang screw hole with clay befor putting on the release agent. You can cut out the bedding in the screw hole after it set's up. Put some clay in the front screw hole and release agent on the front screw. When you drop in the action and tighten it down, the screw will drive the clay plug into the action. Keep the bedding compound back away from the front screw hole, It'll flow there by itself. Just snug the front screw till some bedding comes out around the action, don't tork it down till it's all done. Bedding should also squeeze out around the rear tang. Let the flowed out bedding set up, but not harden, then cut off the flowed out bedding with a sharpened hardwood stick. After several hours, back out the front screw about 1/2 turn then retighten the 1/2 turn. That will make sure you have not glued it in.