I propose that pressing S – with an existing slur (and only that) selected – will advance the reach of the slur to the next note. (Alternatively, if this is too dangerous, make it apply only when that slur has been freshly created and is still selected).
The S key appears to be “dead” whenever a slur is selected anyway, so there’s no “waste” (correct me if I’m wrong). Seems like it would be a nice little micro-feature, akin to the duration double-press for dotted notes, which is a gem.