One problem is that Japanese has an unusually large number of homonyms, and more importantly, these are often homonyms where grammar alone is insufficient to distinguish them. This would make written texts much harder to read without a simultaneous change in how people word their texts.
Possibilities within my idea:
*The 15th-century Portuguese orthography, whilst somewhat reasonably phonetic, wasn't perfect and there were variations even within the orthography (i.e. should "língua" (language) be spelled "lingoa", "lengoa", "lengua", or "lingua", all of which are attested in the manuscripts?), so whatever Japanese is transcribed would be as a Portuguese person would hear and understand it. Of course, too, Portuguese orthography would be heavily affected by the Renaissance in the 15th-17th centuries, which only complicates the spelling even more as silent Latin and Ancient Greek letters are brought back and thus making etymology the main determiner in spelling (until 1911 in OTL, where a major spelling reform in Portugal under the Republic brought back phonology as a main determinant, thus i.e. transforming "bahia" to "baía", "columna" to "coluna", and more extremely the Brazilian state of "Goyaz" to "Goiás").
*The reflection of Japanese Roman writing under this proposal would be Late Middle Japanese, and since written languages are inherently conservative the representation of grammar and the sounds would reflect that even with spelling reforms here and there. In this case, it's no different from Vietnamese in OTL, where their writing system largely reflects Middle Vietnamese (since that was the period when the first Latin-script material was produced, particularly Father Alexandre de Rhodes' dictionary) despite all sorts of spelling reforms and the like. So there's that factor to keep in mind.
*Sino-Japanese, to some, would indeed constitute an obstacle, but the main point to keep in mind is that often time a mixture of context and compounding would probably help. At the same time, there would be an increase in the use of native Japanese words (since ideally the writing system would work if the writing was truly vernacular), so compounding native Japanese words and Sino-Japanese words with the same meaning to create one word could help on one hand. Use of international vocabulary would also help. In reality, however, the homonyms would not constitute a major problem as one would think.