Where is the brooder?
Are you still supplying heat?
If the brooder is in your house, you might be able to remove the heat source. That would let them start getting used to lower temperatures (lower than heated brooder), and would be a good step on the way to moving them outdoors. Excessive heat can also make chickens drink more, so cooling them down a bit might help there too.
(I agree that more space would also be good, and you are right that moving the chicks outside is likely to be the best fix for that situation.)