Not all breeder boxes are created well. When I was looking into breeder boxes, I checked reviews on the one you have and many people state fry can swim through the slots, pretty much making it useless. (though I can't tell if your fry are large enough to not pass through the grating)
If you have a fine pore fish net, you could suspend that in the tank and let the fry live in it.
I guess if you could use string and cover the slots on the breeder box with finer pore material such as cut up fine mesh nets, or even cut up sponge or filter floss.
other than that I guess you could have the fry grow out in another tank (makeshift if you want).
The vents/slots are to allow water flow through it. A lot of plants might obstruct surface agitation, but if the rest of the aquarium has plenty of surface agitation/dissolved oxygen, the breeder box will be fine. Co2 won't be a problem. Stress shouldn't be a problem. I've had fry in breeder boxes/nets and all the fish were fine.