The answer here was exactly what I was looking for, a nice way to turn tiles into actors.
LibGDX: How to make tiled map tiles clickable?
I have a problem with this though, and that is that it only seems to work on one layer. From the code it seems like it should loop through and deal with all the layers, but that doesn't seem to be the case.
My problem right now is that if I add a second layer on top of my main layer in tiled, it will only "see" that layer. It works fine with one layer.
Edit: Both layers will be shown visually, but I can only interact with the top layer. The best thing would be if I could have my top layer be ignored when making actors, because it's mostly going to be used for transparent tiles and stuff like that.