... ... indeed I can?t swap frames because the super is a medium while the brood box is a deep. .......
what?s the damage in the putting the second super too early? This one will not have drawn comb. It?s july so it?s going to be hot, the extra space should not be an issue temperature wise. Are there other issues to be aware of?
Thanks
Wrt box/frame size. This is a reason I promote picking one size for everything. All medium or all deep. Soon as there is mismatched equipment, the flexibility for hive management is hampered and the piece count of equipment sitting around the yard goes up to near double what is actually needed to operate.
With respect to adding more boxes. As said, the timing and intensity of the flow is regional. It may be best to ask some (more than one) beekeeper close to you, such as the bee club, what their past experience is for flows in June/July in your area. Then you can decide how much space is needed. As example: where I am, they need a deep box per week. If I am going to be gone for 2 weeks, they get 2 boxes before I go. Check your local consensus. Any risk of adding too much space is also regional. What pests are in your area that may move into excess space that is not used or patrolled by the bees? For example small hive beetle or nearby heavy ant infestation.
As for lazy bees. .... when they run out of room, frames are pretty much all full, burr comb built and full of drones and honey, .... yes, then they do get lazy. imho, bees hanging out on the porch washboarding is a sign that everything possible has been put in order and they do not have enough work to do. They are bored. Give them more space, give them more work to do. For largest growth and biggest harvest, ensure that they always feel their house is -just- a bit too big and the pantry is never much more than 1/2 full.
Hope that helps!