I have an HP 8903B hooked up to a Rigol DS1104Z scope, similar to your setup. My trace is actually slightly worse than yours!
However, you can definitely clean up the waveform on the scope end with a combination of bandwidth limiting, anti-aliasing, or noise rejection.
I have noticed with many HP pieces, for example function generators, there is often very high frequency junk lurking around. With a low
bandwidth scope, you might never see it. Hook it up to a modern scope (say 500 MHz), turn down the source amplitude to a few mV, and
good luck even triggering a stable trace due to the high frequency noise. Vendors seem to only care about the frequency band that their unit is
spec-ed for. For instance, I have a 40 MHz Wavetek generator that puts out a bunch of garbage at 600 MHz.
All this plus the inevitable ground loop you probably have between the distortion analyzer and scope.
By the way, the 8903B is a great unit!