But in the case of ō, you can only use a doubled letter if the underlying word is おお. If it is おう then you don't have a doubled letter you can use; you need "ou" and that's not Hepburn any more. It is "wāpuro rōmaji" (word processor romaji).

"ou" is fine too, actually. See the proposal p. 14 (=16 in the PDF): https://www.bunka.go.jp/seisaku/bunkashingikai/sokai/pdf/942...

(To differentiate between the case where it's actually two vowels, you have to put an apostrophe inbetween; their example is 小唄 -> ko'uta.)