For the Carrollton, I would lift the toilet off of the Unifit adapter and see if anything is blocking it.
If there is something there, it would tend to catch paper.
Plumbers here know, that even though nobody remembers putting things down that don't belong, we still find them.
In a bathroom with counters, there is always a way.
Sometimes, it's even one of the contractors using it for a garbage bin.
I had one toilet I pulled that had enough carpet strands to do a closet hanging out the bottom.
Under the rim, could use cleaning sometimes.
Dark flecks could be mold.
I've been using Clorox with Teflon.