This is incorrect. I think you defined round-trip as something else, but some character set A providing a round-trip compatibility with other set B means that B

This is incorrect. I think you defined round-trip as something else, but some character set A providing a round-trip compatibility with other set B means that B can be converted to A and back to B without a loss. And it is one of Unicode's explicit goals to provide a round-trip compatibility with major encodings including Japanese ones. Han unification only means that when you convert Japanese encodings (B) to Unicode (A), it is not distinguishable from non-Japanese encodings converted to Unicode. This means that the Unicode text doesn't always follow domestic conventions without out-of-band signaling or IVD or so. But if you know that the text was converted from a particular encoding, you can perfectly recover the original text encoded in that encoding.