I was reading upon Japanese writing system history and found out there were several attempts to abolish the use of 漢字 in favor of kana or romaji, e.g. after the WWII. All of those failed, and the only big thing which happened to Japanese writing system since the adoption of Han characters is the invention of kana. However, I couldn't find information about any attempts to construct alternative writing systems, analogous to Hangul in the Korean language.
The main problem with kana/romaji approach is homophonic 漢字 and words. I can see why this could prevent the adoption of kana/romaji-only writing with additional spaces b/w words: it may be enough for video games but is problematic for news, scientific, and legal documents.
The other thing which strikes me is that hiragana and katakana do not exactly match the phonetic structure of the language. For example, the word 漢字 consists of 2 syllables "kan+ji", but in kana, it is written as "かんじ", which is 3 moras. In Hangul, each symbol encodes exactly one syllable, which seems to the language phonetic system much better. This makes me think that Japanese can be encoded in a similar way. This may be just my personal quirk, but I feel like many 音読み kanji should have been a single kana character, e.g. "かん", "ほん", etc. (However, I do understand why it is not so, so don't bother explaining this.)
All this makes me wonder if the invention of kana was the one and only attempt to address the problems related to the use of 漢字. Are there any academic/historic attempts to invent something akin to Hangul for the Japanese language? If there are, how do they address the homophony problem?
Related question on linguistics.SE: Why was Korea able to remove kanji but Japan wasn't when both languages use homophones?
To clarify: I'm not saying or implying that 漢字 is a bad thing which should be replaced. I'm just curious if there were any "creative" attempts of doing that since obviously there are supporters of such ideas even among Japanese people.
Also, I'm not saying that Korea did a better job (compared to Japan) by introducing Hangul, either. Hangul is used as an example only. No comparison intended aside from purely scientific.