Nice playing! It all sounds perfectly fine to me. But you said you're using a Fender 62 Original on your Precision, and THAT is why it sounds so bright to you. I had one in my Precision for a year before I replaced it with a Geezer, and it's a very bright pickup. It's not a bad pickup, but it's very bright and a little mid-deficient for my tastes. The Geezer is less bright but still has some. The Duncan SPB-1 is another pickup in that vein with slightly less upper mid content than the Geezer. But if you really want to put a darker pickup in it, the DiMarzio Model P is very hot but considerably less bright.