I'm not sure which pot your talking about Hetty. Looks like they all have gorgeous, large plants filling the pots up?
I would use Carol's idea and put more bamboo sticks (closer together) and maybe a little taller than you previously did. If you fill the area with even very short bamboo sticks (so they really don't show much), then the cats can't even step into the pot.
I went back and read your first post, I now understand it is the second pot (not shown in the photo) that you need plant suggestions for.
Hmmm, something large enough to cover the 12" surface. That would do well in your lovely lanai growing conditions.
This will take some research for me, I have totally different growing conditions from yours. On my way to search for something wonderful and unusual.