You gave me an idea!

• Give each obstacle in the initial map an ID, and build three indexes by ID, by row, and by column.
• Use the list of obstacles to build up a map from (ID, direction) to (next ID, direction) (if any) – that is, for each obstacle, update the map entry for any preceding obstacle that could reach it.
• This map can be used to compute the path very cheaply.
• And crucially, you can easily update the map for new obstacles using the same method above.

I think this would give a pretty good speed up, and you might not need to worry about only checking intersections.