There was a recent thread somewhat about this on the chicken forum. If the air inside is humid and the roof is cooler than the air, you are going to get condensation on the inside, or even frost, not matter how well it is ventilated. I get exactly the same thing you are talking about in my coop and under a very open shed roof. If you are getting condensation or frost on the inside and not on the outside, then it probably is a ventilation issue if you have a moisture source inside, like chickens breathing and pooping. I would not expect a moisture source inside that shed, so I'd think it is just humidity from the air.
The only things I can think of are to insulate the roof (which you said no to already), box it up tight where outside air can't bring moisture in (yes, less ventilation), or find a way to live with it.