Hi Poke
I have a regular 686 for IDPA. I bought it two years ago and I finally shot a few IDPA matches this year (I might add two or three with Pizza Bob). They are great guns but a few comments....
My 686 (and the same with my 929 PC), the revolvers out of the box shoot but in many cases if your going to use it in IDPA then your going to need to have some work done on it. I had the exact same problem you had, when clean the cylinder indexed fine but after about 25 rounds it would get tight. I would do what others suggested, a trip to the safe table to wire brush everything. I tried all different powders and charges still the problem was there. Even VV N320 would cause the problem.
My guess is the cylinder is not square to the forcing cone. But it could be something else but I'm probably right on this.
You have two choices really in my opinion. You can send it S&W and you might get it back working ok. Or what I did and if your serious about competing with the gun you should have a pistol smith go over the entire gun and smooth/lighten the trigger. You probably have if it's stock about a 14 pound pull. Both of my revolvers were that heavy out of the box. Of course this option will cost some $$ but worth it in my opinion. If you do lighten the trigger most likely you will have to use federal primers in your handloads.
To give you an idea, I had the action polished and lighter springs (main/rebound) installed, the actual trigger hook polished, the front sight converted to fiber optic, ball detents in the crane for both open and closed position, the charge holes polished and chamfered and the cyl cut for moon clips, the hammer bobbed and an extended firing pin. The trigger is about 7.5 pounds now. I'm not sure of the exact cost but it was somewhere around $400.00 maybe more. A lot of money but totally worth it. I did have to tweek it because I was getting light strikes but its good now.
Cleaning the gun every stage or two while it might solve the problem will get old very quick trust me on this. Spending the money might hurt I know it did for me but once you get over it all is well. I have not had the problem once since and I have had days where I put almost 500 rounds through the gun. Most, but not everyone that is serious about revolvers and shooting new production S&W have had work done on their triggers. Older S&Ws had lighter triggers from the factory, these days they are very heavy, thanks to the lawyers. When I bought my 929 I took it to the pistol smith without ever firing a single shot.
One last thing not to muddy the waters. I think you should rethink your load. I don't claim to be an expert, far from it but I have friends that very accomplished revolver IDPA and USPSA. Go with a faster powder not HS-6 and a lighter bullet. I have spent a lot of time on my 686 load and mine is XTREME 147g plated .357 (sold as a .357 9mm bullet) with 3.3 grains of Titegroup. In my gun this makes power factor. I knocks down poppers but I'm going to at some point kick it up to 3.4-3.6g for a bit more zing. I know some love HS-6 and 158g bullets but it's way more ammo than necessary for IDPA.
Sorry one more thing. As Pizza Bob mentioned about having your speedloaders on the strong side. I agonized over this myself. Again I'm not an expert in any way shape or form but there are a few notables in my club and so my being awful at this sport is not due to not having good solid instruction and/or inspiration available to me. I watched a bunch of youtubes and really wanted to use a strong hand reload but gave up on it for a weak hand it works for me much better/faster.
Here is a vid, granted the shooter (Josh Lentz) is using an illegal for IDPA pouch but he is using speed loaders and he has won many IDPA revolver titles.