Depending on your system it is not unusual that performance various from stocks to indices. Just make sure that you did real portfolio level backtesting with real portfolio money management. This is not only important to determine the real drawdown but also possible profits. Also consider Monte Carlo analysis before investing!!
Non-correlated entities would be Soybeans to the ES or Crude Oil to Cotton or Fannie Mae to Krispy Kreme. Believe it or not the firm I once worked for had a guy who was a Laser Physicist at NASA and he happened to be the best statistical guy I have ever met. His statistical systems that he programmed in Excel were the most exhaustive I've ever seen. He programmed this statistical non-correlated matrix that demonstrated on a daily basis the % or correlated vs. non-correlated and you would be surprised to see the relationship on any given day. Cotton may have a 100% correlation with Copper today and just 1 month ago it was a - 237%. Finding a non-correlated market to trade is tough but it is not just for Hedging. It is to diversify yourself as to take advantage of what is happening across the board.
I am not sure if you are trying to say that correlation is more a question of discretion/logic then of a mathematical figures - if so then I agree. As mentioned before you should test it on a portfolio of various symbols to see the effect also use sound money management.
Seems to me that if you have gone this far in creating and backtesting a strategy, you should by now have an indepth understanding of how and WHY it works, or does not work, in each market you've studied. There is a logic and rationale behind every successful strategy, and you should be able to answer your own questions about where to put it to work. If you aren't really comfortable with that, you probably need to continue your own research. Nobody else can help you with that.