I found an article "The structure of the German root", by Chris Golston and Richard Wiese (published online on ResearchGate in 1998; originally published in the book Phonology and Morphology of the Germanic Languages). The analysis in this article is based on a database adapted from a list made by Wolf Dieter Ortmann (1993), who created his database based on entries in root dictionaries, mainly Augst (1975).
The article has a footnote saying "At a later stage, we plan to make the database available through the internet" (p. 68-Researchgate). I haven't been able to find it, though.
On page 75 (Researchgate), the article says that there were 131 roots in the database with two syllables like Arbeit. This excludes words where the second syllable is schwa or a schwa + resonant/syllabic resonant, but the database includes some items considered "nativized loans" (Golston and Wiese give the examples "Abenteuer ‘adventure’, add- ‘add’, Akt ‘act’, Scharlach ‘scarlet fever’") (p. 68-ResearchGate). Also, the roots seem to be of all word classes: Golston and Wiese mention "[ʔalaın]
‘alone’" as a two-syllable root.
Golston and Wiese say that there were only five three-syllable roots in the database:
The five roots in our corpus that violate the alignment constraints twice are all loans and felt to be such by most speakers: [ʔaleːgʀo] ‘allegro,’ [baldʀiaːn] (name), [ʔɛnziaːn] (name), [feːbʀuaʀ] ‘February,’ and [januaʀ] ‘January.’
Based on this, I'm fairly certain that three-syllable noun stems would be extremely marginal if not nonexistent.
Without a look at the database, it's hard to tell how many of the two-syllable examples are "nativized loans": Golston and Wiese say that the database includes 792 roots of that type, so they could potentially account for almost all of the 131 two-syllable roots in the database.
One other example I found (taken from p. 88 of "Prosodic organization in the babbling of German-learning infants between the age of six and twelve months", by Andreas Fischer) is Hering 'herring', which apparently has an unclear etymology, but which looks like a suffixed word of some type. Honig also looks like it has a suffix, but as far as I can tell it actually wasn't derived that way (at least, not within Germanic at any recent date, since Wiktionary offers a Proto-Indo-European reconstruction for its etymon). König is technically a suffixed form, but I don't think the base is perceived very much or at all by modern German speakers.
One of the examples mentioned in the question, Kranich, seems to have originated as a suffixed form.