Q:

SpaceX's 4,425 satellite constellation - what's the method to the madness?

The BBC article SpaceX aims to launch internet from space discusses the SpaceX proposal for a dense array of over 4,000 LEO satellites for global internet coverage, and links to SpaceX non-Geostationary Satellite System Attachment A - Technical Information to Supplement Schedule S.
The initial configuration will be the first group of 1,600 active satellites (plus spares) as 32 orbital planes of 50 satellites each, all at an inclination of 53 degrees and a LEO altitude of 1,150 km. The final configuration adds to that four more sets of planes at four more inclinations and altitudes, for a grand total of 4,425 active satellites (plus spares).
If I understand correctly, this configuration is supposed to provide global coverage such that any place on earth will see at least one satellite above 40 degrees elevation at all times.
My question is - how does this constellation's configuration actually work? Do these inclinations and altitudes satisfy some expected behavior for nodal precession? Is there some ellegant orchestration here? There are five slightly different altitudes, which means each group will have a slightly different period, so I don't think the different groups are phased relative to each other, only within a group or at least within each plane of each group.
Are there five different altitudes simply for collision avoidance - which is more difficult between planes of mixed inclinations than between planes of identical inclination (but different nodes)? 
Q: How does this constellation's configuration actually work? - what is the method behind the madness? (idomatically speaking)

Here are some simple plots. I'm working on better ones - hopefully an animation or a 2D map with groundtracks.

above x2: screen captures from SpaceX non-Geostationary Satellite System Attachment A - Technical Information to Supplement Schedule S.

A:

Nodal precession doesn't matter for a plane of satellites like this, they will rotate around in unison, so the coverage will remain the same.
Okay, so why the unusual dual inclination constellation? The inclination of a satellite band tends to let you know what latitude it will work best at. A 0 degree satellite works best at the equator, a 90 at the poles. 53 will work best for customers around 40-60 latitude, north or south.
To have complete coverage, there are two areas that can slip. First of all is the poles, which won't receive any coverage at all. A smaller number of planes could cover the poles quite effectively. 
The other is a bit less obvious, but is the equator. The equator will have 32 bands of satellites over it, crossing twice per orbit. In essence then there will be coverage for 64 satellites at a time. Over the higher latitudes, the distance around the globe at that latitude is lower, and thus the density will be higher. A single constellation of equatorial satellites will cover this gap quite effectively. 
Looking at SpaceX's plans, they figure the 32 plane constellation is sufficient for the equatorial regions. The 3 inclinations are 70, 74, and 81, with 5, 8, and 6 planes respectively. My guess is the initial deployment is deemed to be good enough for most of the world's population, but they will eventually want to have global coverage. To do that with the fewest satellites possible, they decided to add in the additional 19 planes. It seems this is required because the FCC dictates that coverage must include Alaska to use that frequency band, which makes things particularly difficult. 
Thinking this through a bit more, it seems 9 lateral degrees is the limit of coverage. Given 53 for optimal US coverage, 81 covers the poles, there needs to be two sparse groups of satellites to cover the rest if the area. I believe the two were chosen to optimize the satellite count by a simulation of some kind.
Note also that the higher the orbit, the more satellites are in the plane. I suspect this is to make up some of the margin that would otherwise have been lost.

