Cluster analysis is heuristic in that you need to try different methods and then see which are: the most replicable (reliability), and the most natural (natural).  You can use the Adjusted Rand Statistic (see Fisher & Hoffman, Psychometrika) to assess replicability.  You would do this by splitting your sample into two subsamples and comparing across the two samples.  You can also compare across different cluster algorithms the same way. The notion is that if you have robust structure to your data, then your cluster solutions should replicate across algorithms.  The critical issue is that you need to make an initial decision on whether you are going to define "similar" as a shape or a distance.  Those two are not comparable.  You assess for naturalness by seeing how other variables vary across your clusters.  Read Blashfield and Aldenderfer (Sage publications) for good explanations.  Cluster analysis is not exactly bothered by dependencies, but having the same variable more than once weights the cluster solutions on those variables even if they are different forms. 

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There are several classification methods for unsupervised learning. Cluster analysis is one. Another that is often used in latent class models, as these can be extended (the taxometric methods of Meehl and colleagues should also be considered). However, you have a fairly clear hypothesis about change in response time. It seems calculating a single measure for each person (in the simplest version, the mean slope of their RT points ... but you might do this with a multilevel model), and then a histogram. Sometimes groups are obvious then, but there are methods to explore if the observed distribution is a mixture of a few distributions.

The data do not conceptually lend themselves to a latent class analysis per se.  The problem is that you do not have enough different variables to make it interesting for a journal article.  There are really only five variables (measured twice).  Even though the computer would do fine cranking through a lca, the classes you would wind up with are not interesting.  There is a form of latent class analysis however, termed latent transition analysis that may, or may not, be interesting that might be worth investigating.  Is the question of comparing the profile of the five variables at time 1 with the profiles of the five variables at time 2 interesting?  The textbook on both of these versions is by Linda Collins at PA.  You would need to download and install their proc in an existing version of SAS in order to run this. 

A mixture model (like the lta) would be answering a slightly different question than the original posed by your original question.  Do you think that the clusters that may result from your original approach are stable across other samples?  Do you want to be able to use the cluster solution in more than one paper to compare with other naturalness variables?  If so, then you may want to stick with the cluster analysis.  The problem with the cluster analysis approach is that usually the naturalness analysis is approached as univariate ANOVAs with the IV being the clusters and the DV being the naturalness variables.  This would not allow you to  talk about combinations of naturalness variables being simultaneously related to your clusters.  If you want to take this approach to your question, then cluster analysis would not be an appropriate method (even though you could run MANOVAs, but they are a little old fashioned and your reviewers would probably recommend some form of SEM).   If you want to consider variables related to your original input variables, then one of the other approaches suggested by the other two reviewers would be preferred.  The issue really is what is the queston you are trying to answer.