Yeah, you can get lower capacitance transformers, also with higher isolation voltage ratings -- not that the latter is necessarily helpful, but the increased distance between windings also tends to reduce isolation capacitance, so it may be some help.
Shielded cable won't do you any good because you're just replacing CM over twisted pair with CM over shield, plus inviting ground loop problems on any units with shielded connectors. Shielded Ethernet is only meaningful (with respect to this concern i.e. conducted emissions within the network) when the whole system (everything on the network) is designed around it. (...Which really isn't saying much of anything, because "designing the whole network" implies the ability to reduce emissions of any given component in the network anyway, and, when is that ever true?)
(The other thing that shielded Ethernet does, is reject external noise from the communications within, i.e. improve CMRR. That's evidently not a problem here, so isn't a motivation to choose it. You'd be looking at that for, like, 30V+ (or 30V/m+ radiated) noise levels, like in super nasty industrial environments.)
As for potential offenders, I've noticed a bit of EMC on my bench before. After shuffling through a few things, I traced it to crusty connectors on the USB hub -- contact cleaner and a bit of cycling later, and it went away. I've used the same hub for many years, so it figures the connectors are starting to dry out, or succumb to fretting or whatever. If you can figure out if the noise seems like power supply noise (switching peaks, or modulated by line frequency or varying load current), communications (erratic, varies with activity?), video (buzzing?), etc., that might give some clues where to look. As in my case, note that all connectors are eventually suspect -- USB especially as they're not anchored or anything (just retained with spring tension), but so too is HDMI for example, and even screw-retention plugs like VGA or [classic] serial can flex enough to wear out the mating surfaces.
Tim