I am glad more folks than I see this as a need to go to a permit draw system.
given the facts as stated in the question I see this as the only logical decision. I was short on time when I posted, but was able to pick the land game animal I think best mirrors the data set.

"Between 2,400 and 3,200 mountain goats are estimated to live in Washington."
"Females (or nannies) do not breed until at least 2.5 years of age"
" longevity is normally 10 to 13 years"
" Kid and yearling survival may be less than 50 percent depending upon the severity of the winter."

" Current permit levels are conservative and represent no more than four percent of mountain goat populations that are surveyed regularly and are stable or increasing"

"Mountain goat populations have declined overall in Washington relative to estimated historical levels. Goat populations within the state were considered to have exceeded 10,000 animals (including those within federally-managed areas) as recently as 1961."

http://wdfw.wa.gov/living/mountain_goats.html

I also found that they give birth normally to one kid each.

using those numbers the recruit to parent ratio would be something less than 2. (average lifespan, one offspring, <50% survival= less than 4 adults per breeding pair)

Permit draw is tried and has been working for a lot of years. if we want the chance to kill a wild steelhead (rather thru catch and release or for the meat) on this river ever again it is the only option that makes sense.

Here's the kicker as I see it. Will it save the steelhead population for generations to come? NO. there are to many other stresses on the Steelhead's Habitat be it ocean, river, or estuary. the reason the goat population stays as stable as it has is the simple fact that it's habitat is relatively untouched. We don't yet build houses on top of mountains, or dump our toxic waste on them, or spill oil on them. but we have pushed them to the fringe. hence the population shrinking as the human population has grown.

It is time to face the fact that Steelheading as we have known it is at an end. without augmentation there will be no fishing for them except for the lucky few or the criminal. With augmentation it is still going to crash, only in a different way. My 1st "Home river" has a decent population of Native Steelhead. with no hatchery plants for several years now. I am going to fish it this year for the first time in a few years because it is still open, but I don't expect to catch anything til January. My 2nd "home river" gets a nice hatchery run but in the last 10 years it has gone from 8 guys fishing the areas I fish to 30 guys these are daily numbers. the catching level has mostly stayed the same. 0-10 fish a day depending on water level and luck. that made for some great days for the 10 of us. but even a good day for the 30 of us leaves many skunks. It is simply the way it is now. get used to it or get out.