Not to discourage you, but I think you need to interface with the respective taxon curators under mammals, reptiles, fish, possibly birds etc that you want to add things to.
Even though your species are extinct, all these areas and others are locked taxa, which means only the designated curator in those areas can add any new records under them.
You can see who the designated curators are by going to any of the respective pages such as https://www.inaturalist.org/taxa/26036-Reptilia and on the taxonomy tab clicking the Taxonomy Details link.
You know your right, apologies for wasting all your time. The original goal i thought of was Inaturalist is like the only site where you can make lists of creatures, and i think that inaturalist would be more complete if all species where in the database. So if you wanted to make a list of bacteria you could.
iNaturalist is a great tool for managing taxonomy, but because the focus of iNaturalist is to document living organisms, our taxonomic tree is geared towards supporting living organisms. The few extinct organisms we have are largely the consequence of imports from Encyclopedia of Life and because people like to upload photos of fossils on occasion. It’s really only out of courtesy that some extinct organisms are in our database. I’m sorry if this disappoints you.
However, iNaturalist can always use more curators and your enthusiasm is appreciated. I would suggest applying your focus towards living taxa, rather than long-extinct ones.
Have you considered getting involved with MyFossil? They are building a fossil database and social network and would be more up your alley. Also, if you want to volunteer with a participating lab, the Paleobiology Database is building a database of specimens from scientific publications.
There is the fossil genus Exogyra, in its phylogenetic context with other bivalves. Now imagine if I had observed several genera of Gryphaeidae, as well as other families in the Ostreoidea. They would appear in their proper places as branches on the tree. Is there a database for fossil observations that has a comparable functionality, that is, one that would let me look at my observed taxa in the form of a phylogenetic tree?
I was going to ask this question in one of the existing threads on fossils, but they are all closed. Anyway, this is my concern with being redirected someplace away from iNaturalist.
On MyFossil, you can view your own (or other users’) specimen lists (not a life list per se).
You can even generate little specimen cards for them to print and organize your collection! There is also a taxonomy view, not shown as a nice tree though, just a list of the clades. I haven’t uploaded my collection there but have been meaning to…someday.