@oralloy,
First, the P/Tr extinction didn't just happen overnight, by some estimates based on volcanic complexes, it could have started five or so million years earlier than when it became the "boundary event"
Second, There were so many families like Sphenacodonts which contained at least 6 sub families of these synapsids that one or two genera ( at least to me), like caseids or sphenacodonts. lived up to the end and some of these looked all the world like dimetrodonts except for their stupid faces.
Remember, and Im not fully convinced, That all fossil genera are based upon a couple of skeletal remains and any differences are assigned new species names. Its often time that some paleontologist wants to be memorialized for findng a "newbie" when it may just be a deformed form.
When Cope found his first dimetrodonts in the Red CliffFormation, the chronometry of that formation does reach into the middle upper PWrmian , so the dimetrodon story is still full of ignorance on all our prts.
I cant help you much because I don't use many vertebrate fossils in my ork because usually mineral deposits aren't associated with most vertebrates (eceptions being cichlid fishes and sygnathid fishes (pipefishes and seahorses).
I know of 6 different genera of synapsids that hd those big sails and one or two lived into the Induan of the lower Triassic.
Third,I think the artist on the program couldn't have chosen a more representative fossil for the late Carboniferous than the synapsids or therapsids, so why not a little artistic license on his part.?
Personally, I would have plopped a couple of big-ass Permian Opistoparian trilobites (which classically defined the GREAT DYING). But, it wasn't a geology lesson, it was entertainment with a little science thrown in.