If you would have one beat a few milliseconds off, would that turn your 6/8 into e.g. 619/824?
There is no strict boundary between which streams of sound are music and which are not, so have fun analyzing whatever else will come up.
If I were annotating it, I would use some ad hoc notation. I would probably just say 13/16 with a note to add a quarter beat (or something like that) to the end of each measure. Another option might be decimal signatures, like 13.25/16.
