The other thing about using too much 'artificial' (as they call it around here) is that the grass it promotes can be too fragile for hay. Hereabouts we have to work our hay hard in order to dry it, and a bright green sward pretty much crumbles to dust under that treatment.
You probably have much better hay-making weather than us so may not need to turn it more than once or twice, in which case it would be less of a problem.
You'll probably do much better with re-seeding (have you thought about doing some aerating first?) as you are doing, and an occasional load of FYM from a helpful neighbouring farmer with a muck spreader

The other thing to think about is inputs and outputs. If you are taking nutrients out of the equation you need to put them back. So if you take a hay crop off, you remove nutrients (in the grass) and need to replace them. But of you only graze it, the grazing animals are putting back pretty much what they take out in their dung

, so it won't need a lot of topping up, certainly not every year.
BH does use artificial, but tiny amounts and not every year, and generally only on areas that we take a hay crop (or silage) from.