A verb for “to walk” in The Etymologies of the 1930s under the root ᴹ√BAT “tread” (Ety/BAT).
Neo-Quenya: For purposes of Neo-Eldarin, I assume ᴹ√BAT is for a “heavy walk” as opposed for √PAT for a “light walk” or “step”, so I would use vanta- for an extended or serious walk, and thus including “✱trudge” and “✱trek”.
A word appearing in the Declension of Nouns (DN) glossed “beam of wood” (PE21/27). It had a stem form of ramb- and a longer variant ramba, but in Tolkien’s later writings ramba was “wall”.