Wow, you made me realize that I forgot a crucial bit of information: you control the player with the keyboard (up, down, right, left), but I won't allow him to leave the paths he's moving on.
Also, the paths will be set in the level, I don't actually have to programmatically (if that word even exists) generate them from the intersections. And there's only one level, so not a ton of work to build them. Ogmo aligns things really nicely.
I guess I'm trying to figure out, given my objectives, how best to combine Entities (representing individual objects or Tilemaps) to give me the flexibility I need for all the collision detection and calculation required for my game. And because how I lay out my level in Ogmo -i.e. what layers I use - also influences my choice of Entities (since I will parse the xml and convert all the various elements to Entities), I need to make the right choices upfront.