I know goats will eat buckthorn but in my limited experience they will eat everything else first. Does anyone know if they will focus more on buckthorn either in the early spring when it's the first to leaf out or late fall when it's the last thing hanging onto it's leaves?

We have around 100 acres to clear of it and it seems impossible. The neighbors also won't do anything about it on their land so it will need to be continously managed

Grazing is considered somewhat effective in knocking honey suckle back but is not really good at eliminating it. Also with 100 acres that is a lot of area to cover and it will take a lot of time or you need a ton of goats and that means a lot of fencing unless you don't care if they our out a lot.
There are types of Round Up (glysophate) where you can spray and kill the growing vegetation and graze or cut 3-4 days later which may work in keeping ahead of the emerging plants. Downside is you will have killed all the other vegetation as well.
Bryce