Firstly, well done on choosing fantastic livestock, we have togg goats and a Bagot billy who is just fab!!
Do they have a hay rack?
It might be an idea, then fill it to the top and judge how long it lasts. If they are hungry, they will eat it.
They really don't like wind and rain, so don't worry about it, just give them a "path" to field that keeps their feet dry.
How old are they?
Youngsters (maybe like children?!) go through phases of what they will try to eat and what they don't.
Chop "sticks" of carrot (round bits might get stuck) and add to the hard feed.
most veg seems to go down better here when chopped up. And bananas, and the skins are the absolute favourite!
Any chance of posting up a photo of your Bagots? What line are they?