Insects in general avoid petroleum. It clogs the pores and suffocates them. I have been painting the legs with a generous dollop of petroleum jelly in a ring, which worked for me in Florida but isn't having the same effect I thought it would for my bees. Putting grass in the moat would defeat the purpose, because the ants would just use that as a bridge.
I don't know what the stand looks like, but I suppose the best thing to do would be to cover the moats with a funnel, like the ones you see on bird feeders to keep the squirrels out. You would want to keep a space between the moat, and the "roof" so the ants would have to bridge it to get to the hive.