I bet Little John would have some ideas on it. The fellows on that side of the pond are famous for messing around with different styles of division boards and cell starters.
Hi Frank
Was just passing ...
I have an assortment of Cloake Boards: some full-sized; some full-size & divided which take two nuc boxes on top; and a couple of single nuc-box size - all of which have gates. Some of those gates are hinged, but most are removable. I like having gates on those boards as it then makes operating the slide a breeze.
But - other than those I don't use gates, as most of my stackable boxes have 22mm holes (wine cork size) drilled in 'em, which are used as entrances, and corked-off when not required.
I run top bee-space here, which means I can make simple flat Crown Boards (inner covers), and in order to make similar simple flat Bottom Boards, I've made up a large number of 15mm (1/2"+) shims which sit between the box and plain bottom board to provide the necessary clearance. Each hive entrance is via the holes mentioned above, which also have anti-robbing screens placed across them.
With regard to double-screened boards, I don't have any - but I have quite a few single-screen boards. Some have 4" squares of (what you call) hardware cloth, and some are large sheets of steel mesh which started-off their life as fire-guards which normally surround open fire-places.
So - if I ever need a double-screen board, I simply use two singles with one of those 15mm shims in-between.

That way, I can still still use the singles for combining. A more flexible arrangement, imo.
'best
LJ