In native Japanese words (that I know of at least) like 通り and 大きい, to elongate the お-sound, another お is added when written in Hiragana (instead of う like in Sino-Japanese words). However, it just crossed my mind that the volitional form ending - which should certainly be natively Japanese - follows the 漢語 pattern (e.g. やろう).
Is this a remnant of the old auxiliary verb む mentioned in the answer of the post Origins of the Volitional Form?
As you note, there are two modern patterns for spelling //oː// in kana: [CONSONANT or VOWEL KANA ending in //o//] + お, or + う.
This was originally the volitional auxiliary / suffix む, which attached to the irrealis or 未然形【みぜんけい】 ("hasn't happened yet") form.
These are sometimes the result of an earlier manifestation of this same "//a// + nasal" sound shift, generally occurring at the time of borrowing. 王 is one example, realized in Middle Chinese as something like //huaŋ//. Japanese speakers may have heard this more as //waŋ//, but earlier Japanese didn't have any ん sound -- so the Chinese term was imported into the Japanese sound system as //wau//, with the earlier hiragana representation of わう. Due to the //-au// → //-ɔː// → //-oː// sound shift described above, this became //wɔː// and then //oː// (since //wo// doesn't really exist as a phonemic sound in Japanese).
Alternatively, they may have been //-ip// or //-ep// in Middle Chinese. That final //-p// became //-pu// in Japanese, and then as //p// shifted to //f//, final //-fu// softened further to //-u//, and then we see the same //-iu// or //-eu// to //-joː// shift as above. 協 is one example, realized in Middle Chinese as //gep//, giving rise to the 呉音【ごおん】 reading of ぎょう.
Some of these arose from the same //-iu// or //-eu// shift as above. One such example is 今日【きょう】, reconstructed as //kepu// in the earliest form. These are spelled with the う as the vowel lengthener.
Others arose from a related shift, where the mid-word ひ or び of 人 would shift to ふ or ぶ, and then result in an ending of either //-uto// or //-udo//. Examples include 素人【しろうと】 (from しろ + ひと) and 仲人【なこうど】 (from なか + びと). These are also spelled with the う as the vowel lengthener.
Still others of these arose from the lenition (softening) of a consonant, such as 遠【とお】 from earlier //topo//, or 頰【ほお】 from earlier //popo//. These are spelled with the お as the vowel lengthener.
There are other patterns that also occurred, as in お父【とう】さん. An earlier form of 父 was //toto//, and the honorific form during the Edo period was //otossan//, from a contraction of the second //-to// with the //s// in suffix //-san//. During the Meiji period, this //otossan// was reworked by the Ministry of Education into //otoːsan//, which was spread via textbooks as the new standard form for this word.
If you dig around in a monolingual Japanese dictionary, you'll find that the entry often starts with a hiragana spelling that differs from the expected modern spelling. See the 大きい entry at Weblio, for instance, which starts with:
おおき・い おほきい ［3］ 【大きい】
That second kana string is the old, pre-reform kana spelling, and those old spellings give you some clue as to how the term was pronounced in earlier stages of the language. These can, in turn, help explain the derivation of the long-vowel readings.
The premise of your question – that in native Japanese words long "o" sounds are always spelled by adding お rather than by adding う – is simply incorrect. (Consider the verb [儲ける]{もうける} and the nouns [お父さん]{おとうさん} and [素人]{しろうと}, for example.)
That said, the う that occurs in the volitional form ending does in fact derive from the auxiliary verb む, as explained in the sources quoted in the post to which you have linked.
