The root ᴱ√MUKU “cacare [Latin = defecate]” appeared in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. múko “dung” and ᴱQ. muqa “filthy” (QL/63). As there are no other roots of similar meaning in Tolkien’s later writing, I think it is worth retaining a Neo-Eldarin root ᴺ√MUK for this purpose.
Primitive elvish
muk
root. cacare [Latin], *defecate
A neologism coined by Paul Strack in 2022 specifically for Eldamo to replace G. gorn “dung”, the Sindarin equivalent of [ᴱQ.] múco “dung”.