Finally, we found a point of compromise.
How is 見出す different in connotation from 見つける?
Also, do you know any historical information as to why it is usually pronounced みいだす instead of みだす (having a long vowel instead of short, as it is pronounced in 見る)？
見出す is closer to “to get insights”, “to find implications/potentials” or “to dig something from the deep side and bring it to the surface”. 見出す requires a more creative way of thinking. For example,
進むべき道を見つけた = I found a passage (in a forest etc.)
進むべき道を見出した = I figured out what I should do (e.g. career path/goal).
その科学者は新しい星を見つけた (or 発見した) = The scientist discovered a new star in the sky.
その科学者は新しい星を見出した = The scientist found a great potential in the young guy (i.e. a great candidate for the next-gen leaders in the academic field).
If you pronounce みだす instead of みいだす, it’s most likely to be interpreted as “to start watching/looking at”. It’s the same pattern as 走り出す (to start running) and 笑い出す (to start laughing). みだす and みいだす are just completely different words.