"We can know God. Just not necessarily empirically in a way that is without dispute."

Again, I must disagree. Jesus, Buddha, Lao Tzu, Rumi, Shankaracharya, people who wrote Pentateuch and Upanishads, all talk about the same and agree. My personal realization also agrees with them to a T. The way to reach that realization is then, as I said, almost scientific -- theories are falsifiable, the process is repeatable, the actual knowledge allows formulation of predictions, etc. As I also said, the only difference is that the results are (for obvious reasons) not recordable.

And just as a side note -- knowing in "heart and experience" is empirical by very definition. However, the knowledge I'm talking about is, indeed, beyond experience and perception in general (no matter how farfetched or copout-ish it may sound).