Just discovered this forum in my search for info on affordable varminting scopes, etc. You fellers are a whole couple classes above this poor sot.
I have been known to bring home Wyoming speedgoats on a windy day from Kaycee, maybe not over 500 yds., but near 400 on the run. A 150 BST 300WSM might be a bit much for the little fellers (ok, ok, its my elk gun too), but its also a bit much for the wind - sure flies nice.
I think your biggest challenge will be their jumpiness, your shot may be on the run. They don't like it when they can't hear you cuz their ears are whistling in the wind.
Your other challenge will be changing conditions and variability of temps. That clay becomes some of the slimiest stuff on the planet - looks ok, butcha can't go nowheres.
Good & versatile transportation is a must. Um, for many reasons:
We carry coolers with block ice with us, holds a quartered lope nicely. We get 'em on ice within 1/2 hour, keeps the taste from going gamey. The first year we went, my mentor didn't - drove around with my goat in the back of the pickup on a cool day, became a somewhat unpopular dinner at home. The cooler makes the difference. So does the "GoatHoist". (no trees, and goat hair flies ALL over the meat otherwise)