A good test for ventilation in the summer is to walk into the house on a warm summer day (or at night). It should be no hotter inside than out. If you can feel a change and it is hot and stuffy in there, you have a problem. Birds will notice it too and will avoid using it if they have a better option......trees, rafters in a well ventilated run, etc. My daughter's first flock preferred to roost on top of a plastic playground set....on the roof of the fort. She was frustrated they were pooping on the playground set (the stuff runs downhill.....who knew?). They were frustrated they didn't have a better option.
You also appear to have a black shingle roof over plywood. That will absorb heat from the sun and radiate it down into the house, so you are fighting that too. Good in winter, not so good in the summer. If roof is shaded by trees, that will help a lot with the summer sun.
But if it is hot and stuffy in there, short of swapping out the roof, best option is to really open it up to let the hot air out. Gable vents and such. If the back part is really secure, leaving the doors open will help too.
PS: You might want to move those nest boxes up so the bottom of them is about 18 inches or so off the ground. But leave the tops of them no higher than the roosts. Not sure where you found those, but as nest boxes go, they are about the perfect size and shape, including the sloping roof.