Think you could work on floating the barrel yourself. Some carbon black on the barrel to see where it contacts the forearm and a little sanding till it no longer touches and you are done. I had problems with a barrel that would act similar to yours. Sent it back to the manufacturer who said the barrel was bad and replaced it with a barrel that shoots great.
If you had experience shooting shells you reloaded you would understand why one type of bullet shoots well and others do not. That is the reason why Browning has that Boss thing. I am not expert but read and heard enough to have a basic understanding. When your bullet goes off it starts a resonance in your barrel. Depending on the bullet and speed of the powder etc your bullet can reach the muzzle when it is dead center or at the outer edge of the vibration and off course anywhere in between. So when you shoot the same bullet with a variety of powder charges you will see some groups are not so good and some are great. The better groups are the ones where your barrel is consistently in that same spot. So that ammo you found is just more consistent in your gun.
When I had very similar problems Free floating the barrel was the most common suggestion
Oh and one other idea is if you get something like the lead sled or something similar you will remove you from the equation. I have a rest that has a shock absorber and you can shoot any gun with no recoil.
I would give floating the barrel yourself a shot and if you still have problems and want to have it bedded I would also have them look at the chamber to see if ti might be distorted in some way. Oh my son's gun shoots great but after the 5th shot it shoots like a dog. When he cleans the barrel it goes back to shooting great.
Might want to clean after every three shot group. You are probably just waiting for the barrel to cool anyway.