In general, swinging flies isn't a numbers game (although you can have some stellar days doing so especially at this time of year). When you're purely swinging flies, you're trying to illicit a chase response, a reflex response or an aggressive/territorial response from the fish. Swinging flies usually works best on fresh, untouched/un-fished for steelhead that haven't been pestered by other baits, lures or flies. If you're looking for numbers of fish, nymphing is definitely more consistent. Run an egg pattern, nymphs, michigan wigglers, woolly buggers, stoneflies, etc either under an indicator or dead drift them without an indicator.
There's one guide who fishes the Huron tribs who uses a technique called "Swymphing" which combines both a dead drift and a swing at the end of the drift. You can try that with whatever flies you already have.