If you are looking to remove carbonates or hard water build-up (lime/scale/etc) using an acidic solution would probably be the easiest.
I'm not familiar with dragon stone, but with a quick image googling, seemed like a wide variety of rocks being called dragon stone. ADA lists theirs as being inert, but some of the pics I found looked like weathered limestone, so depending on where you got your stones and how much you trust the source, you may want to be careful using an acid.
I'd also recommend not using toilet or other household cleaners - a lot of them have dyes and perfumes added that could be hard to remove from the rock. Not sure about CLR, as I haven't checked the labeling.
Usually you can get a jug of acid (HCl?) reasonably cheap at a hardware store - I think they use them in pools a lot, or cleaning up masonry. Don't do this unless you are familiar with the safe handling and disposal of acids.
You may be able to just use a strong vinegar solution - I've read of people using this to treat concrete tanks and ponds before adding fish. requires a bit of monitoring the pH and changing the solution out as it rises, but is a lot safer.