That's interesting about the compounds in some water binding with copper. Goats do need a lot of copper! And goats can also be very picky about drinking water! There's likely a correlation.
Rain water sounds like a good idea. If you have a clear/white drum you can just paint it blue or black or
berm it with substrate or
straw. Burying/berming it will help keep it cool, too, in the summer.
Another alternative is to find a good loose mineral that's really high in copper. I've only ever found it in locally formulated loose minerals. Big name brands like Mana-Pro are really low in copper. And just let them free-feed on minerals as needed.
In my goats, signs of copper deficiency in the past have been hair turning white, "fish tail" (hair missing on tip of tail), and increased parasite loads. Loose minerals have corrected these things throughout the years.