It definitely wasn't fat because stirring didn't solve anything, and also, it actually tasted watery.
Jygach, the original recipe called for pomegranate molasses but said you could substitute balsamic. the lemon juice was included either way. Again, I'm not sure that was the issue, because it wasn't just textural, it actually tasted watered-down.
I did run it thru a fine-mesh sieve, and it's considerably better now. I think next time I'll leave the red peppers laying out after I peel and slice them, I really think that was my error.
Thanks for the suggestions, everyone! Very much appreciated.