Greg, I'd just scuffle up the top of the soil in that planter to discourage the moss. (although it doesn't hurt anything) Be careful not to go too deep to damage the roots of the plants. Maybe spread some fresh, sterile potting mix on top, with some extra Perlite in it for aeration.
Also, the plants in that planter are things that like sun, does the planter get some sun during the day? That should also discourage moss. If you don't want to move it, how about cutting a branch or two above there, to give it more sun? It's a lovely planter, but looks like it would be a beast to move. Maybe just plant something that likes shade instead, that will fill up the spaces. Then either the moss won't grow at all, or at least you won't have to see it.
But commercial potting mix is generally sort of acidic and if it is staying moist all the time, it sure will grow moss.
