I would give that a try but if doesnt work i would give them back their lamp and put it or a timer for the night and slowly cut back a half hour every night till they get used to it.
Nitrogen deficient. Get some Miracle Grow they will perk up. Or go to your local feed or hardware store and some kind of additive that is high in Nitrogen Bat Guano is high in Nitrogen but be careful how much you use you can over do it with Bat. no more that a Table spoon per plant mixed into...
Steam is a last resort and you have to be very careful not to burn the chicken never do it over the stove or anything boil the water take it out to the coop the cold air out side will help with the steam and the water will cool quickly. LAST RESORT ONLY!!!! its better than takin a chance on...
Egg bound try holding her over some steaming water becareful not to burn her but the steam and warmth will help ease the egg out. never break a bound up egg it will 9 times out of 10 kill the hen