I think that you are on the right track and the question should end "and just made one long composer name" (not "or").
You see the dilemma that only very few players can deal with multi-value fields. That is why you see only one if you use that feature.
If you merge the multi-value fields to just one (and get one long string), then you get the phenomenon that some players split this long string into separate entries and others leave it in the original long form.
And then there are players that can deal with multi-value fields but show them as a merged long string.
And there are players that use the long string for one kind of display and the split one for other views (WMP does).
WMP does the split
iTunes takes the long string
foobar can deal with multi-value fields.
And MP3tag can help you to get the best solution for the abilities of your favourite player.
(BTW: for players that split strings, it would be "semicolon-space" as separator)