How to characterize the regularity of rhythm?
You have already found train of intervals between the events. What you are interested in is a respresentation of that in time. I would suggest, from my experience, to run a sliding window differential filter, with some low pass averaging filter at the output, that will give you the rate of changes in time. In this way you will get the rate of changes as they progress in time, which is most likely what you actually need. Yes, standard deviation may be done, but that is just one number, as you said, and that is not sufficient.
One simpler method will be to use just a sliding average window that averages train of intervals and gives that as a result.
With this, youy may, at the end, postprocess obtained result, by finding max. min. and average values, as the informative, yet simple measurements of the signal that has been analyzed. 
If needed, you may get more complex solutions, involving cyclostationary data analysis. In a nutshell, finding some statistics functions, (sorry it cannot be avoided if you decide to go this way): for example mean, variance, cyclic correlation function, cyclic power spectral density etc. This will lead to a rate detector, with various outputs that characterize the signal rate changes (and much much more). I hope that this helps.