The drawing of large genealogies is not easy, and phylogeneticists (among others) have tried a number of solutions, including circular diagrams as we as interactively zoomable displays. One interesting solution that does not appear to have yet been used in phylogenetics is the concept of GeneaQuilts.
These were introduced by the Visual Analytics Project:
A. Bezerianos, P. Dragicevic, J.-D. Fekete, J. Bae, B. Watson (2010) GeneaQuilts: a system for exploring large genealogies. In: IEEE InfoVis '10: IEEE Transactions on Visualization and Computer Graphics, Oct 2010, Salt-Lake City, USA.The web page has a video introducing the concept, which does a better job than I can do here. The basic idea is to abandon the tree / network representation, and to use a diagonally-filled matrix instead, where the rows are individuals and the columns show parent-offspring relationships.
Here is an example genealogy, based on the reported relationships among the Greek Gods.
If the relationships are tree-like then the diagram will be concentrated on the diagonal of the matrix. However, network relationships (inbreeding) will cause off-diagonal elements, two of which are shown in the example: one involves Hades and his niece Persephone.
Several, much larger examples are displayed on the GeneaQuilts website. There is a program that can be downloaded, which takes as its input standard family-history files.
There seems to be no intrinsic reason why this display form could not also be used in phylogenetics.