Whenever our troop camps, it's always for 2 nights. We NEVER do a one-night campout. I would highly recommend getting in at least 2 2-night campouts as you suggested. Unless your are an LDS Troop, i don't see why they wouldn't want to stay another nite since they go thru all that work setting up camp!
Personally, i think the monthly camp-outs is what keeps our boys in the troop, and in scouting. When the boys are at camp, they are different then when they are at home, it's hard for me to explain but, it's like their own little getaway, away from home, homework and yes, mom. I feel like everytime my son comes back from a campout, he's grown a little more .
Sparkie
P.S. Our boys are ALWAYS working on Merit badges (whether in camp, or weekly meetings) the first one being....First Aid.