How about a Maranta, aka prayer plant? They stay pretty low, the leaves are fairly thin though but quite broad. They make a nice cover for the lower parts of a viv but not great as stand alone perches.
There are trailing kinds of Peperomia obtusifolia that don't grow very tall, the leaves aren't enormous but are very fleshy and sturdy. The upright versions might work for you as well- it takes a few months to hit your 18" mark, then you can just cut the top 5" or so off and stick it back in the ground.