jouless

Polylabel is pretty great

https://github.com/mapbox/polylabel

the cycle has an inside and an outside, so only half of it is reachable. you could draw it with fat lines to remove the ambiguity. as you showed in your image though, you can get to most of the accessible parts only after you've escaped the maze. to make it a proper maze with one entrance and one exit you'd want to use the interior of the cycle as the maze and cut entrance and exit points, maybe the exit being at the farthest flood fill distance from the entrance.