As oil supplies are tightening everywhere, does this mean that an additional part of "standard logistics" will become waiting on (decreasingly available)lighter crude to mix in with heavier crude for refining (so, higher stocks in general)? Or sending heavier crude longer distances to specialist heavy crude refineries?
Actually it is already standard practice. Yes, it must increase as heavier supplies are substituted for any present lighter feedstocks.  Refineries with only light processing capability must be modified, or new refineries capable of working with heavier feed blends must be built.

I designed 2 adjacent pipelines in Venezuela.  One from a marine terminal for light oil, delivered from the good quality Mesa fields, and take it 140 km inland to the heavy oil Zuata Field.  The light was blended with the heavy (APIº9.6   bitumin) at the production facilities in Zuata.   It was then heated to min 175ºF to decrease the blends viscosity to levels capable of being pumped via another pipeline back to the marine terminal.  This process was changed later to use naphtha in place of the Mesa crude.  An adjacent separating plant was started up to separate the naphtha and recycle it back to the Zuata field, where it is blended again.