I think it is a mistake to assume that the mathematical contingencies of a model necessarily provide a better description of our reality than those we are more at home with.

Whilst the mathematical model is absolutely crucial in physics and science in general, we would be fooling ourselves if we felt that it is reality rather than merely a very good way of making predictions.

I think a philosopher, a poet, and a mad computer all have as much to say about whether time exists as a physicist. I would however very strictly draw the line at allowing them to determine what goes into a physical theory. the general covariance of GR and possible timelessness of canonical quantum gravity are crucial to a modern theoretical physicist; but, epistemologically, that knowledge is contextual and not universally applicable through all human pursuits.