Have you tried a different scope?
How about making sure the blocks and rings are tight?
Besides a new bedding job that is where I would look.
I thought along these same lines after I had posted last night.
For what it is worth here are some suggestions to try before you take it to the gunsmith.
1. Check the scope ring bases for tightness. On the front base remove the front screw and check for it hitting the barrel threads. If it is the threads may show a slight crushing and the screw may show some marks on the bottom where it has contacted the threads. This can really create havoc with groups since the front base is not tight if this is happening.
2. Check the screws in the rings to be sure they are snug and not letting the scope shift.
3. Try a different scope, preferably a "known good" scope. If you do not have one laying around then take the scope off your 243 ADL and try it on another rifle of known accuracy.
I ran into a scope issue recently which caused me to scratch my head just a bit. I wanted a bit more power on my 223 for shooting groups, I removed the scope on the 223, installed what I was sure was a "known good" scope and instead of shooting 5 shot half-inch groups it was now shooting inch and one-half groups. Since I had not shot the rifle for a few months I checked action screw tension, bases, etc and tried it again and the results were very similar to what you are getting - sometimes 3 or 4 close and a flyer or two, but no real consistency. I used the old trouble shooting technique of going back to the last thing that was done before the issue occurred. I put the original scope back on and was right back to shooting one-half inch 5 shot groups.
Sometimes you cannot even trust "known good" scopes and it is necessary to test them on a different rifle.
If you do these things and you see some improvement or consistency in the groups then you can try the rifle in the other stock to see what occurs then.
Just some more food for thought.
drover
