As far as the barrel channel is concerned - just free float the barrels. Open the barrel channel up so that the fattest barrel is free floated and then when you swap barrels you have no worries. Savage/Stevens come with free floated barrels to start with. On both of my rebuilds, I opened the barrel channel on the stock so that the barrels were free floated. I bedded the action and behind and below the recoil lug, but no bedding beyond the bottom of the recoil lug - the barrels are totally free floated.
As far as a fixed barrel nut - I never gave it a thought. It might work. There are several ways of fixing the barrel nut to the barrel. Welding scares me, you would need to be careful about not heating the barrel up much, because it could cause it to warp. Once a barrel is warped, you will find it not to shoot very well. It would be right at the chamber, I would think that a chamber that is "bent" would cause all kinds of problems. Maybe a better way to go would be to epoxy the nut to the barrel with JB Weld or similar type of bonding material. You could also cross drill it off center with a roll pin in the hole. You do not have to really jamb on the nut to get a good fit. It only has to be tight enough to take all the slack out of the threads and the barrel not move during firing. I can get into all kinds of technical descriptions on thread engagement - but threads are not a precise fit. You need to deform the threads a little to make sure they are all engaged all the way around and up and down the thread length. If there is any play in the barrel/action joint, it will play havoc with accuracy. I have not tried it, but you may be able to get enough torque on the barrel with strap wrenches. You maybe able to make "spanner" wrenches too. Use one of the gas blow by holes on the action and drill a hole in the barrel nut for a spanner wrench (once you have fastened the nut to the barrel. I would think that you would need to have a consistent torque from one barrel change to another and back. You maybe able to index the barrel and action with a "mark". Once you have the barrel set to the correct torque scratch a line between the barrel nut and the action on the underside, so that when you refit the barrel, you come back to the same mark each time.
Another though on quick change barrels - use interrupted threads, like on Hornady's Lock 'N Load dies. I am not sure if there would be enough strength left as more that 50% of the threads would be machined away. It might be a problem on large diameter head cartridges and high intensity (high pressure) cartridges. You would torque down the barrel properly and the make a mark on the nut and action. fasten the barrel nut to the barrel with a pin. Then take apart and machine away enough threads in the action and barrel so that they could slip together and then you give it a half turn or so to tighten the barrel to the action - back to the previous marks you made so your head space would be consistent.
I am not advocating the use of any of these thoughts - that is exactly what they are thoughts - food for thought. No practical tests or even running numbers on thread strength or barrel pressures.
Good Luck and Safe Shooting