Sorry, I thought this was solved but my foliage really does look like Corylus (hazelnut) even though stems look like those on Ulmus alata! My foliage is much wider and less regular than that found on Ulmus alata.
Yes Growin, you finally got it, both nature of wings and leaves were troubling me. Ulmus alata has two opposite wings, here they are irregular corky in U. thomasii, larger and broader leaves, clearly unequal at base.
Ok, growin, I think you got it and thank you. We have an anomaly here. Look at geographical distribution and you will notice that Ulmus thomasii is found 2000 miles east of California! Also, literature says that this tree is not found in commerce, i.e. nursery trade, which means that it is probably from a seed that somehow hitched a ride West!