I stumbled across http://biorxiv.org/content/early/2015/09/09/026476 today. This paper attempts yet another method of summarising trees, this time using what the authors call "Spectral Density Profiles", which are just [if I understood correctly] a transformation of the eigen values of the patristic distance matrix.
This seems to me like a principled way of introducing branch lengths in, for example, the sprspace framework: one could store the set of spectra for a particular topology in a hashmap and then use those to inform clustering on the SPR graph. The communities in the graph would then be not only a result of their proximity in the topological space, but also on "branch length space". Their methods are even implemented as an R package, RPANDA.
I'm looking specially at you, @ematsen, @cwhidden, @mathmomike and @mtholder.