Can't speak to the goat harvest but bison would not be hard to implement. Yellowstone would be a tag I would love to have for a cow bison.
Why not let the state in which the animals are located manage the hunts.
Congress would have to rewrite portions of the enabling act of 1872 in order to allow for hunting inside of Yellowstone National Park. It is highly unlikely that the first national park would be opened to hunting given the advocacy against that, and the unlikelihood of congress to find the votes to pass such a bill.
My understanding is that for bison that leave the park, it is up to the states to decide, but of course you have a ton of pressure from the livestock industry to not let them roam around much outside the park for fear of brucellosis transmission. So if you're looking to kill 900 bison and use hunters, you'd have hunters lined up along the boundary of the park and it would look terrible for hunters. The Buffalo Field Campaign loves to film whatever happens to the bison that leave the park and dramatize it. They do the same thing with FWP and Dept of Livestock, but at least they're govt agencies that are used to getting black eyes in the press. And just imagine if NPS allowed it inside the park.
Largely, yes. Bison are a much different "animal" than elk, deer, wolves or bears, however, thanks to brucellosis & it's effect on the livestock industry. Bison in Yellowstone are managed under the
Interagency Bison Management Plan - as one friend put it - a 50 year plan we're 20 years into. This plan calls for culling of animals once they are over a certain threshold.
Over the last 15 years or so, MT has been trying to expand the zone of tolerance outside of the Park for bison to utilize during the winter months, in hopes of both increasing hunter opportunity & harvest and to decrease the need for culling. On top of this, there is a quarantine program in place for bison that come out of the park. Those animals are quarantined for around 5 years to make sure they are not exposed to brucellosis. If they are, and they test positive, they are slaughtered with the meat generally being sent to various first nations for their use. It has taken a helluva long time to get to a point where those bison that are tested & come out clean are able to be sent to first nations with bison programs so they can take the overflow for their herds. Things were going well, until the previous SOI got in the way and set back translocation efforts over a year.
The point about hunters lining up for a firing line is spot on. That's why increased tolerance surrounding the park for Bison to have winter habitat is vital for bison conservation around YNP now, and why we need to think about trans-locating bison to areas of the state, and country, that can support a wild herd of bison.