Good job :3
Also, good catch that 大 = oo (おお). It certainly isn’t ou.
That’s a flaw of the ō romaji: you get used to ō = ou, but actually ō = oo as well. It’s a “lossy romanisation”, you might say. Even more so to just have o = お = おお = おう.
Really, ō should be reserved for ou (おう), if that’s more common, and oo should be covered by another character, like ǫ (おお).
That’s one reason I thought it was better to use the more faithful ou / oo convention.
Compare also the romanisation of せんぱい.
sempai is a phonetic transcription, but it’s obvious that m = ん.
senpai is orthographic, but chooses not to distinguish ん explicitly from n-series kana.
sen’pai does distinguish ん, but the information is redundant due to context.