As often happens, formulating the problem in terms of graphs could have helped in gaining a clear picture and an intuitive grasp on the problem.
However, after having achieved clarity on the high algorithmic solution level, turning back to actual implementation often requires further thinking, designing, and the willingness to go for smart or at least suitable choices.
Shall we explicitly work with graphs in our implementation?
That would be a bad idea.
We better launch a sort of DFS on just the bidimensional array representing the field.
We discover here once again that DFS is not just a specific graph algorithmic but is a more general paradigm of algorithmic solution addressing a wide range of uses.