I think they'll be able to fit in there OK, might be a squeeze for a larger bird...only time will tell for sure.
Have you played with rolling an egg around in the nest and into the trough?
The trough cover looks a little flimsy, is it hard to access the eggs in the trough?
Went to the website...wish they had better pics, hard to see how the eggs are protected or how you access them.
Also how the nest insert looks and whether it's removable for cleaning.
7" high opening does seem kind of small....but might be OK depending on inside clearances.