Hey Dirty Harry
I Live and have grown up in Mt Beauty, (but have only recently started to get into prospecting).
As a couple of other members have pointed out, the rivers are on the exempt list and tributaries are in the national park,
but from what i have known and researched, there realy is not enough gold to worry about looking in the rivers or streams anyway.
The west kiewa only had one reef found in its shed, and that was the red robin mine, it took Bill Spargo, 20 years of tracing minute traces up the west kiewa to finaly find it.
The west kiewa is now part of the Kiewa hydro scheme (so gets diverted and regulated), so hasnt been flushed in the last 60 years,
There are old stories, of some of the early hydro workers trying there luck, but with very little reward.
The Tawonga mine was situated up behind the old Bogong pub at Tawonga, there are two main shafts that go into the hillside, one would be about 600m and the other close to 1Km, but to this day i still cant find any record, or even stories of any gold being pulled out.
Iv'e done some test panning at redbank, (20km form Beauty) and have only ever found the finest flour gold and only a couple of specks, my conclusion is that there is gold in the valley, but it shed very early in evolutionary terms and is sitting in the bottom of the valley (two hundred + feet down).
The (Crusher) at tawonga was owned by the Hamiltons, and was a sand and gravel quarrie, that supplied the needs of the early hydro scheme and local tradies.
if you are in the area and want to catch up give me a PM.
best of Luck
Boyd