I've thought a little bit about your ideas on whole genome phylogeny before and I think it's computationally crazy.
Maybe you could tell us what you would like to discover by doing this? Are you just trying to understand the relationship of the organisms you study, in a taxonomic sense, or are you trying to understand how genome rearrangements are shaped by (or shape) the relationships of organisms. I guess I am not certain what your question is and how we can help you.
I know DNA-DNA hybridization has been used for a long time (since the early 70's I do believe) to understand species phylogenetics. Re-vamping these ideas, like the link you point out does, could be very interesting.
I think computationally the best we can do now is large suites of appropriately chosen marker regions (the emphasis here should be on phylogenetically informative sections of the genome which generally will be based on how broad a level of phylogenetics you are interested). You can do this using lots of programs such as PAUP, MrBayes, RAxML, etc., etc.
I think that looking at genome rearrangements can also be phylogenetically informative, and there are lots of ways to do this also. One of my favorite programs to use now for plants is SyMAP.
This is a huge area to investigate so feel free to give us more information on what your goals are. Good luck!