Oh, so that's while spelling rather than speaking? There's an implied soft "r" there for sure. If it were an extra "r" you were adding in pronunciation, I would have assumed "strategry". It would make sense that as the craft of a mason is masonry, the craft of a strategist is strategry.
And there are some phonemes that just sound more correct in English. As a child, my younger brother used to pronounce (and possibly still does) "museum" as "newseliam". I used to assume it was simply because he's ignorant, but on reflection, I think that it was because he just has less exposure to Latin than most people. Because he's ignorant. So "museum" simply appears wrong to the language bits of what passes for his brain.
I don't think that trips him up too often these days. I can't imagine him in his back yard, can of lager in hand, ciggie dangling from lips, grunting to a neighbour "Garn down the newseliam t'morra, eh?"