Lp governs spots and characteristics.
PATN governs white/pattern.
Beyond that, you are asking for the impossible - at least at this time. The problem is PATN is a complex, and depending upon the sequence of the nucleotides (cytosine, guanine, adenine, and thymine) of the DNA in the genes involved, and the genes themselves involved (PATN involves multiple genes), PATN can exert different influences on the pattern. To my knowlege, that is all we know definitively, although the Appaloosa Project is conducting ongoing research to try to define exactly how a particular pattern is turned on.
As if that isn't enough, varnish roan is thought to be on a totally different gene, which further complicates the pattern issue.
As to your question about why some lines result primarily or exclusively in leopards, it is thought that the lines involved result in a consistent PATN that results in the leopard pattern.
As you can see, it is a difficult genetic issue to figure out, and there is not nearly the interest or funding available for specific horse genetics as for human genetics. If there were major funding for such a project we would have all the answers now, but I don't see that happening in the near future.
If you have an ongoing interest, you can become a member of the Appaloosa Project, which is conducting research on PATN at the moment...