Although I'm the worlds biggest fan of Auto RX after all the engines its revived for me, if you are going to be yanking the blamed heads anyway and have concernes about your rings, why dont you just pull the whole engine, for one thing, its easier to swap the heads with the engine out anyway, then go ahead and pull your pistons and get a new set of rings and run a ring groove cleaner around all the pistons. ( spend a few extra bucks and get a set of gapless rings, you wont be sorry ) . Yea, yea, it would be great to rebore for an oversize etc, but if cash is a concern, and it was running fairly acceptably, honing the cyls out and popping new rings in will breathe a lot of life in. Considering that you are going that far in anyway.
You are not going to break the varnish off by a light soaking of anything, it is a rock hard sticky coating beneath the rings directly on the piston grooves, and you can plan on spending up to an hour with a groove cleaner on some pistons. Teh reason Auto Rx and some other flushes will work is the engine is heated up and teh rings are under pressure and *trying* to flex while the cleaning is going on so the rings act like a wire brush along with the cleaner. If you just set some cleaner on some heavy ring varnish, you might loosenthe outer layer, but you are not going to get enough off to make much of a difference.
Now if you just want to wait and get it back together and THEN run a couple treatments of auto rx, that would be the most successful method without having to tear into the bottom end, but wt this stage I would still seriously consider new rings since you will be halfway there anyway, and its a great time to get rid of all your other minor leaks and seeps