Maybe a dynamic factor analysis (DFA) would help? I don’t have any hand-on experience with them to say if they’re suitable for sure, and it is rapidly approaching Friday evening, but I am aware that they model N time series as combinations of k latent processes, k << N, so it’s something of a dimensionality-reduction technique. I don’t know if you can fit a DFA and then use it on a new time series or what.
I’m only aware of them in the R world, but as a reference here’s A Very Short Introduction.
Also, here is a study that uses DFA that seems like it might relate to your issue, but it’s been on my “to read” list for 2+ years now.
And it might be worthwhile to look at the R Task View on time series, which ought to provide some ideas.
Although you mention non-evenly-spaced observations, which make me think of CAR (continuous AR) models.
Hopefully this is useful, until someone more well versed comes along.