I see, then, you can only use "hitori" and "futari" in standard modern Japanese. "Mitari" and "yottari", at the most, might be used by old men in some regions very occasionally.
12ヶ月(12 months) in old counter system should be "
too amari futatsuki" not "totsuki(also not tootsuki) amari futatsuki." The latter would mean "10 months and 2 months."
Ah, as you might know, "yamato kotoba/wago" is the term for native Japanese words. It's the antonym of 漢語(kara kotoba/kango); Sino-Japanese, not the language used in an era.
Japanese language - Wikipedia
These terms(yamato kotoba/wago, kara kotoba/kango) may fit your context rather than the term like "on/kun" or "origin."
The reason;
The word describable only by kana is never called "kun-yomi."
The Japanese origin word like 会社(kaisha) is also classified as "kango"; 和製漢語(wasei kango).
While you're so interested in Japanese language, why don't you use kana/kanji? (sorry, just curious)