Appropriate similarity measure that highlights symmetrical values of features
Is this an issue of features?  From the explanation, it seems that the feature you are considering is distance. So the results are as expected (from a "bag of single feature distances").

You mention that order is important, so that can added as a feature.  Or since you mentioned "phase shift", time (and/or frequency) -- giving you a time series.  In both cases, you then can bring in all kinds of tools.  You could start with regression and go from there to more complex methods (simple sometimes is best).

That would allow you to yield similarity metrics between single or multiple vectors.

Vectors contained in a sliding time window vs. population, is something you maybe can also consider, we did a solution like that once.