I am not getting that VECTORS entry at all.  My plan looks just like yours after you got get of VECTORS.  I made the turn to TRYSH ok, everything was looking good, then for no apparent reason, the plane turned to the right about 90 degrees and headed for TOY.  

To be clear -- am I supposed to leave it in LNAV mode all the way to the ground, or should I be switching to APP mode at some point?  

I just tried a different plan, going from KORD to KCMI with the ILS 32R VEALS transition.  It turned towards VEALS on final and started to descend from 2600, but it never managed to get to VEALS and lined up for the landing.  It crashed in a field about a mile from the runway.

SO am I doing it wrong by leaving it in LNAV the whole way?  This is an important point.