We only access models via experiences. If you aren't willing to reduce models to experiences, why are you willing to reduce the physical world of apples and automobiles to experiences? You're already asserting a kind of positivistic dualism; I see no reason not to posit a third domain, the physical, to correspond to our concrete experiences, just as you've posited a 'model domain' (cf. Frege's third realm) to correspond to our abstract experiences.