This is just a bit of idle speculation on my part as a former astronomer, but I wonder the extent to which the LIGO pipeline allows for non-zero eccentricities

This is just a bit of idle speculation on my part as a former astronomer, but I wonder the extent to which the LIGO pipeline allows for non-zero eccentricities in the orbit. Because the signal-to-noise ratio is so low the pipeline has to find events by matching the observed data with precomputed templates. Thus in some sense you need to already know what you're looking for in order to find it. My understanding is that the LIGO team generally assumes that the orbits are perfectly circular before merger. This is normally quite a good assumption because gravitational waves will circularize the orbit, so if the orbit began with any modest eccentricity the eccentricity right before zero would be nearly zero. The interesting thing is that if the original system was not a two-body system but was a three-body system, then the influence of the third body could have driven the inner two to extremely high eccentricities (say, 0.999). Although gravitational waves would still reduce the eccentricity, there could plausibly still be a residual eccentricity of ~0.1 at merger. It's not clear to me how signals like that would match with the pre-calculated templates. Back when I was in the field (four years ago now) there was just starting to be a pretty good awareness in astronomy about the importance of three-body systems for various astronomical events, but I had the sense that that awareness hadn't yet spread to the LIGO community.