I'm surprised the File Exchange Control Panel didn't do the trick. The problem of LW documents has been around for some time. I have a suspicion it's a Java problem where it strips the files of their properties. I've discussed this a no. of times on the forum over the past few mths. The ultimate fail-safe technique is to use a file utility (I use Mac Army Knife) to change the file's attributes to what they should be. However this might be a bit technical for some people. MAK is easy to use however. Do a search on the forum for this app. Using the file Attribute Editor, once you've re-added the file properties such as type & creator, the appropriate icon returns & will open by that app.
I'm not sure QT can play all types of mp3's anyway!! And there are many types. You might hate the suggestion but how about obtaining an mp3 player that can play all. I'd recommend Audion which can also play formats that iTunes can't even play such as OGG Vorbis. The newest version (v3) can also recognise the newest format of mp3 Pro. It's called os9 version but is compatible with os8.6. Whenever you open a file with Audion it changes the icon to that of its own so it'll always open it by default. (But I think you can change that in prefs.) You'd just drag & drop your mp3 (with its blank icon) onto audion.