For the variable selection part of your question, maybe try using the Partition platform, or the Factor Screening Utility (Analyze, Screening) to pick out better variables. A decision tree (and if you have JMP Pro, Bootstrap Forest or Boosted Tree) can out perform a logistic regression. The bootstrap and boosted trees nearly always out perform the logistic method. In these model platforms, look at the column contributions to find the variables that explain the variation in your response best. (these things are all in JMP 12 and 13.)
The Ordinal Logistic regression assumes a sequence to the levels because its calculating the probability of the next higher level, not the probability of each level. Its not always a good solution, but it might be possible to cluster your levels into just two groups so that a nominal logistic is possible?
JMP Systems Engineer, Health and Life Sciences (Pharma)