I would say, if you're running shallows for brood, then you need to run at least three and preferably four boxes. I would get them strong and gang busters in four, maybe five, then reduce them back down to two or three using a queen excluder, just before a nectar flow. This would build them up strong in numbers but then reduce the brood just before a nectar flow so you would get more honey stored instead of nectar fed to young larva. The numbers of boxes and timing all depends on nectar flows and length of season in your local.
I run screen bottom boards here, can't say as I have an opinion about them. They are needed for powder sugar dusting for varroa treatment, which I did last year but not this year.