Your tank is pretty small for any anemone, unfortunately. BTAs don't stay small and cute, as you've seen in my Nano. And due to the flow in your tank, I don't know what anemone would be happy and not wander everywhere (including your overflow).
Clowns really don't care and will host in anything (including a clam or inside a M. capricornis which I've seen at my LFS' showtank).
The mesh may be a problem. Eheim Sponge would be better in the long run, and if you get a couple of pieces you can just swap them out weekly to avoid trapped detritus and nitrate issues. Just insert it inside the overflow behind the teeth to keep the clowns in the display section.
Whatever you do, be aware that if your 'solution' restricts the drains, your tank will overflow.