If your goal is to make a "true" Indy movie, as it could have been released by Spielberg and Lucas (only trying to have a better cut), I think you should NOT use TOD or Crusade music. Because I don't think it fits "Indy canons" to use other sequels musics (maybe I'm wrong but I can't remember a TOD music in Crusade). And even the Ark theme in Crusade is only used as a quick hommage. Same thing for the Crusade music on the picture of Connery in Indy 4.

But if your goal is trying to make the film better from your point of view, no matter what, and if you think music from TOD and Crusade would be cool, I'd say why not.