I'm still unable to get the two layers back to where they were a few weeks ago. They continue to get worse by the week 😞
I've followed your suggestion, ordering the geometries by the districts they are in, proved by using the TOP keyword in SQL Server. After rebuilding all the indexes the issue persists.
The display of the data in ArcMap is actually really fast. But adding it to ArcMap takes minutes. Just selecting it in ArcCatalog freezes the application for minutes. Other layers in the database, even fairly large ones, are instantaneous. This all makes me think there is some cruft in the SDE tables, or at least something wrong in them.
I've tried copy/pasting them into a new layer or importing into a new layer (even without the GlobalID field) and the new layers are just as slow.