I think the bottom line is that excess filament starts to harden just as the nozzle moves to a new location on the print. In addition to what's already mentioned, I'll suggest trying to adjust your retraction settings. It could be that you're not retracting far enough or attempting to retract too fast.

Simplify3D has perhaps the best print troubleshooting guide I know of. Even if you're not using Simplify3d as your slicer it can be a handy reference for suggestions on fixing print quality issues. The legs of the chair in the sample print for the stringing or oozing section have the diagonal build-ups that you're describing.