For everyone's benefit, I am following up with some results:
Between Paxar and VW, it was determined the the files exhibiting extreme slowness had "Unified View" disabled. It should be noted that our workflow is 2D (3D modelling is done in Sketchup) and as a result, we have never really paid any attention to that setting. From the best that I can determine, it was disabled when the users in question created Saved Views, and the "Save Unified View" checkbox was checked. Therefore, even if a user inadvertently enabled the setting, each execution of a saved view reset it it to disabled. The result was a slowdown in large files that made the application unusable. Curiously, we did not experience the same degree of slowdown in VW2013.
Our files are regularly between 75MB and 120MB in size and make use of between 20 and 50 design layer viewports, with many of those referenced.
Since fixing this (by simply enabling Unified View), we are seeing performance in line with expectations, and are enjoying the new features of 2016. Of course, it will take time to transition all of our projects into the new version, so we may be reporting back more info as that happens.
Many thanks to the VW tech team and Neil at Paxar.