These are maybe 1/8 inches in diameter an inch or so tall. Growing in leaf litter beside very well rotted logs, probably white oak (majority of trees here)

to american Xylaria species in Mycotaxon 26 (1986). It’s based on substrate and spores, but the species are also grouped in macro characters (size and shape).
Other species with the same thick stromata as polymorpha (> 1 cm) in that key are allantoidea, grandis, poitei and schweinitzii. More slender species with similar shape are cubensis, curta and longipes. For a proper ID, microscopy of mature specimen is needed.
I’m sure some more species have been discovered since then too.

To start with, what is the size of these specimen, and what do they grow on?

http://mushroomobserver.org/45771
http://mushroomobserver.org/66648
http://mushroomobserver.org/66141
http://mushroomobserver.org/57540

but I agree that there is probably way more speciation to Xylaria, even in North America, than our handful of commonly used names suggests.

of Xylaria species. Why do you expect this to be polymorpha?