Thanks to PA4TIM for alerting me to the delay line's failure mode.
Thanks to oldway for locating the specific Bench Brief describing the issue.
Thanks to tautech for the pointer to a replacement delay line.
Remarkably - to me - squeezing the delay line
has magically[1] cured the problem. The risetime is back to slightly under 3.5ns, rather than the anaemic 7ns yesterday.
Given that the manual states the delay line is ~100ns long, and it looks like it is only ~2.5m long, I wonder what secret sauce they use to get such a long delay.
[1] as in Arthur C Clarke's third law