As a fellow Montanan the point on how many non-fishing water users is a good one. Fishing is pretty minimal compared water skiers, jet ski's etc. There are many places though (Noxon Reservoir on the Clark Fork as an example) that contain Millfoil which is on the move in NW Montana and it's a big bass tournament lake which has fishing boats coming an going all over the place. The state is now setting up check stations but these IMO aren't numerous enough to really do the job.
Educating people in masse is what needs to happen. Make it part of licensing, posters in retail outlets, mailings and enforcement. As stated, fly fishing gear is just a tiny part of the big problem, the whole movement needs to be ratcheted up to apply to everyone using our water resources.