Let me draw a horrible mspaint graphic depicting this...



Ok so start at "start" and we're headed to "end". Place a vector going directly from start to end and check for the closest vector intersection. In this case it is vector AB. Now, using the endpoints of AB, we draw two more vectors to end again and check these two vectors. Immediately, B is not usable since it goes through (itself) another block (it might be possible to use the vector below AB, but I'm not sure how to obtain it at this point). So we use A. Get the closest vector intersection from A to End which is vector CD. Use the end points of CD and shoot two vectors to end. C is unusable just like B was so we use D. Get closest intersection from D to end which is EF. Use end points of EF and shoot two vectors to end. E is unusable like D and B so let's try F. Success! F to End is clear.

Final path: Start, A , D, F, End.

No idea if this is feasible at all. Just the first idea that popped into my head.