The root ᴱ√TYOSO appeared in the Qenya Lexicon of the 1910s with the gloss “cough” and derivatives like ᴱQ. tyos “a cough” and ᴱQ. tyosto- “to cough” (QL/50). I think it is worth positing a Neo-Root ᴺ√TYOS to salvage these early words.
Primitive elvish
tyos
root. cough
A word appearing as ᴱQ. tyos (tyoss-) “a cough” in the Qenya Lexicon of the 1910s derived from the early root ᴱ√TYOSO of the same meaning (QL/50).
Neo-Quenya: I’d retain ᴺQ. tyos “cough” for purposes of Neo-Quenya from a Neo-Root ᴺ√TYOS.