Clustering Multi-Variate Time Series Data

My end goal is to plot a PCA like plot (2D scatter plot) for my 3 variable time series data to see if there are natural clusters in the data. I don't have any sort of classification sorted out yet, just raw data entries.

I like the idea of using DTW for each signal, resulting in a cost or distance result for each signal (3 values). From there I would then run PCA on the 3 cost values.

The hangup I think i'd run into though is that with the DTW analysis I'm comparing one data entry to another and it would become computationally expensive to compare each entry to each other.

By performing the DTW calculation on just one entry to all of the others, can I assume two entries with similar distances are similar enough? I am afraid that you could have two totally different signals that have the same distance result which would not be what I'm after.