Ive found from experience that resting a one piece barrel on a sandbag in a Major caliber is a simply excellent method for just trashing the accuracy. With my 6 1/2 inch model 610 shooting the 40 S&W, sandbagging the barrel will cause the groupings to double in size. If you're not aware of it, a revolver barrel will "ring" or vibrate when the bullet is transitting the barrel. In addition, the muzzle end will whip around a bit during the transit. Put any restraint, such as a sandbag, against the barrel and ANY variation will cause it to throw the bullets differently with each shot.

In addition, the power to barrel mass ratio will cause this effect to increase as the power is increased. This is why your 686 grouped better with 38 spl. than it did with the Magnums.

First tip, use the sandbag as a rest for your hand and keep the barrel free of any contact with a support. While you'll see more movement of the barrel due to tremor, you will see an improvement in your groups in spite of that tremor.

Second tip, PRACTICE. As I found out with my 6 1/2 inch 610, longer barrels are MORE sensitive to recoil management than short barrels. Since the bullet spends more time transitting the barrel, this means that you have to put in the time to achieve a consistent response to recoil. It is critical and it becomes MORE critical as barrel length increases.

BTW, as an experimient I tried two different approaches to recoil management with my 610 using the 40 S&W. Method one was to NOT restrain the muzzle flip to any great degree. Method two was to manage the recoil as I normally do when praticing Combat shooting and keep the muzzle rise to a minimum. At 100 feet there was a 12 inch difference in the point of impact. If anyone ever tells you that recoil management isn't critical, they have no idea what they are talking about.

PS; I also have a 620 with a 2 piece barrel and that one can be sandbagged effectively with 38 spl., with the Magnums shooting it free of any support groups slightly better. I also have a 6 inch 617 and that one groups best with the barrel sandbagged. Point is, what works best is dependent on barrel construction AND the level of energy expended. In some cases the increase in stability of supporting the barrel will yield better groups, however as power is increased supporting the barrel will likely cause inferior groupings. Where this point will fall for you will likely be highly dependent on how much basic tremor you have in your hands. In simple terms, don't be shy about trying different approaches.