I have been building customs on the 77/22 rim and center fire versions of that action and have developed an accuracy package that really works. This is how I would proceed. You already have a good barrel. The action is not sagging due to flex. This Ruger action is super strong. More likely the tennon to action fit is a little loose allowing it to droop. Bedding the barrel will not help that. On the rim fire version the first thing I would do is check the headspace to see where you are at. I like to set them right at zero headspace. That is controlled by the depth of the recess in the bolt face. It might need faced slightly to get the desired clearance. I then set the barrel back into the bolt so it takes about 3 pounds of pressure to close the bolt against the back of the barrel. This takes up all slack in the bolt and creates a very positive lockup. On the rim fire the barrel is a slip fit so once the numbers are all good I would clean both the barrel tennon and action up sterile and set the barrel in the action with Marine Tex. Put the action in the vice vertically and find where the barrel sits centered and balanced in the action. We don't want a leaner. Wait 24 hours to cure and then install the barrel clamp and torque to no more than 30 inch pounds. Let the epoxy do it's job. It will hold that barrel secure even without the clamp bolts. In a wood stock go ahead and bed the action only and fully free float the barrel. The rear of the mag well is the recoil lug so pay particular care to this area. A layer of electrical tape around the rear tang. You don't want a secondary recoil lug there or it will crack and chip the stock. Then do a trigger job to the desired weight of pull. Save your money on trigger parts. The factory pieces can be made to work as good as anything you can buy for it. I've tried them all. I can get 1 to 2 pounds out of them. Lap the rings to about 90%+ contact on the lower rings. Be sure to use a quality grease where the bolt pivots and on the locking lugs. Now prepare to be amazed. It should shoot sub MOA at 100 yards for 10 shots assuming the barrel crown and chamber are done up nice. I've seen 5 shots groups in the .2's but that is not very often. After this is all done any fliers will be from wind, follow through or ammo. In doors at 50 yards it should shoot them into one very small hole shot after shot.
If the barrel ever needs removed, heat from a heat gun will loosen it right up. I use my Cerakote oven when I need to break one loose.
