The problem I see with Hepburn romanisation would be having to use "ō" in the non-unicode field. tangorin's style of romanisation avoids this and I believe it is actually closer to osu!'s style of romanisation than Hepburn, but I don't know what it's called.Using ō causes all kinds of problems, like confusing oo and ou, nevermind the fact that osu's systems don't like it. Long and extended vowels should always be written out.
In a more specific example of HujuniseikouyuuP, I believe there is reason to start romanising it as FujuniseikouyuuP instead. However, this would imply ふじゅに (fujuni) as opposed to ふじゅんい (fujun'i), so there is still the question of we should use apostrophes in these situations, like with ren'ai. Then there's capitalisation. Is it wrong to use FujunIseiKouyuuP to denote the separate parts of the name? And capitalization issues carry over to many other cases.
For FujuniseikouyuuP, I believe it got romanized into Hu just because typing 'hu' into the IME puts out ふ [fu] as there is no 'hu'. 不純異性交遊 is read FU.
As for apostrophes. This comes down to personal preference I guess? I mean I see nothing wrong with using them, and they serve an actual purpose, but they aren't entirely vital to reading or transliterating. I guess in the Example Fujun'iseikouyuuP I would vote in favor of using them, as it helps break up very long names. On intercapping long names; I've never actually seen anyone do that. I wouldn't be opposed to it, but like I said I've never seen anyone use intercaps in romanization.