Update!
The suspension was pulled out this summer and sent to a local damper shop in DFW for a full service. No damage was found on the dampers, so a service was all that was needed. After the rebuild we also reworked the front setup to add slim bump stops (at my request), needle bearings, and spring isolators for better street manners. The rear mounts looked to be in good condition, but we'll check again when the suspension comes back out again in another 3-4 years/15k-20k miles.
The car drives excellently again, and the suspension is quiet now. The performance had degraded more than I realized now that everything is fresh again, but even just before the rebuild the performance was still good. I wouldn't be able to touch this level of performance for what it cost to rebuild these dampers.