IMO many have a misconception about the accuracy benefit of a long barrel.
With a longer one piece barrel the amount the barrel deflects when a bullet is transitting the barrel INCREASES, meaning the muzzle deflects more from it's neutral point. As a result longer one piece barrels are MORE sensitive to load selection. If the bullet is timed in such a way that it leaves the muzzle while the barrel is passing through it's nuetral point, accuracy is quite good. However if the timing isn't right for the harmonics of the barrel, accuracy can be rather poor. What this means is the load development and testing become critical as barrel length increases.
The most significant benefit of a longer barrel is the longer sight radius they provide and the increase in potential velocity that they can offer. However, you can't take that velocity increase as being cast in stone, you may be caught between acceptable accuracy at a lower velocity or poor accuracy at maximum velocity due to poor harmonics with that faster load. As for the benefit of the longer sight radius, with the optics available today that benefit has basically become outdated.
Finally, as I have learned from experience, longer barrels are more sensitive to recoil management skills. It's because the bullet spends more TIME in the barrel where how consistently you manage the recoil determines how accurately you can actually shoot.
Now, I'm not saying that a 6 inch 686 can't be used to take a white tail deer, too many people have had great success with this combination. What I am saying is that the longer barrel will NOT provide a "magic answer", you'll still have to put in the time and effort to gain the skills to make it effective.
I also think that you may be underestimating the actual full cost of this conversion. It's not a simple matter of unscrewing the old barrel and screwing the new one on to the frame. It will have to be "clocked and fitted" to the frame and cylinder, which requires a precise detail oriented smith with the tools and training to do it properly. I'm guessing the total cost of doing this will run between 300 and 400 dollars but that's just a guess. I would advise that if you want a 6 inch 686 to go out and purchase a 6 inch 686 and keep what you have now as it is. There are plenty of the long barrel 686's on the used market and it's not at all hard to find one that's barely been shot.
Fact is that I found my 6 1/2 inch 610 a real challenge to my shooting ability and it took more practice than I expected it to in order to get moderately good with it. I suspect that you'll find a lot of 6 and 8 3/8 inch 686's on used shelves that were sold because the owner just didn't want to put in the effort those long barrels require.
