I think "Gen Z" (by itself) gets commonly used for exactly the reason you cite: that terms such as Zoomers, Centennials, and iGens are only starting to percolate their way through the zeitgeist.

But I stand by my assertion that "GenZer" shouldn't be used, due to the sociological juxtaposition as well as the phonetic awkwardness. After all, there's a reason why we don't refer to Millennials as "GenYers"...