I have fished the Brule for several days each of the last 2 falls. I know several of the people that guide the river and what they like to use. I can maybe steer you in the right direction as far as fishing the Brule for Fall Steelhead. I would assume these would also work for spring Steelhead.
Egg flies and Nymphs are the go to flies. I don't know how close you are to Superior but Matt at the Superior Fly Shop is one guy that guides on the Brule. He can be very help for as far as flies go. Give him a call, He's a great guy, He'll point you in the right direction.
here is a link to Superior fly shop
Superior Fly Angler