I would be fine shooting that buck on public with only a day left. However I think he would dodge the arrow! Pronghorn are wired and I swear their eyes are so good they see the arrow coming and sidestep it (unfortunately I know this from experience)
As wary as those goats are there's not a shot opportunity for me on any of em at that range. Guessing 35 or so yds? I haven't shot at lots of pronghorn but I have shot at enough to know their reaction time makes a spooky whitetail look like it's moving in slow motion. It's difficult to pass on shots you'd normally take on a deer, but it's not a deer. that's just how I would handle it .
I would wait til he is not looking....allow for the reaction and let her rip. Decent public land goat....1 day left and frontal shots are deadly if you`ve done a lot of them. You are either going to kill him or miss completely.