Thanks for the email prompt.
My experience with SSH and other ordination methods is biased towards community compositional data, not the taxonomic interpretation of morphometrics (although I did give KYST a run in 1986 on the UTAS mainframe using morphometric data.).
I was interested in Mike Palmers take on this issue (http://ordination.okstate.edu/overview.htm):
‘… the number of dimensions worth interpreting is usually very low.’ and ‘.. Third and higher axes can be constructed. The choice of ‘when to stop’ interpreting new axes is largely a matter of taste, the quantity and quality of the data, and the ability to interpret the results.’.
My experience suggests that looking at 2-3 dimensions is a pragmatic but reasonable start, and if the other interpretation statistics look problematic, think about the properties of the data and how you are treating it.
Lee I was interested in your comment about stress values ideally being <0.15, and putting aside how stress is measured, I have generally used a rule of thumb of 0.2, although for large data sets exceeding 1000 objects, this is often a real struggle.
I hesitate to say much more without a better understanding of the mathematics of ordination methods.
My vote is therefore for 2-3 dimensions.