"I know of no significant contribution or advancement to science that came out of a philosophy department" What an incredibly shortsighted comment!
Though not from philosophy departments themselves, Einstein's analysis of simultaneity in special relativity, of general covariance in general relativity (based on the point-coincidence argument), Boltzmann's analysis of entropy, Bohr's formulation of QM (and many of Schrodinger and Heisenberg's contributions), all resulted from epistemological (conceptual) analyses - in many cases there debts to philosophers, especially Hume and Kant, were directly acknowledged.
"fine guys, from an epistemological perspective you are both correct, let's continue business as usual" - I don't recall saying anything of the sort.
"Reality does not care about our physical theories and our understanding of them." -
Do you want to provide an argument for this assertion? Defining what you mean by `Reality', 'physical theory', 'our understanding of them', and the relationship between them? Then we can talk.
As Ian rightly says, the scope of the essay competition is much wider than you suppose.