The Trans Manager looks like what I want. I've downloaded and installed it, now I just have to try it and see. It doesn't seem to be loaded with features that are (to me, at least) useless. I read the user's guide, it seems straightforward enough. I didn't see where it was possible to re-arrange the play order of the tracks... I'll have to play with it and see.

Thank you for the link.

Edit: I can drag tracks within the Trans Manager window to set the play order. iTunes is no longer installed on my computer!

tanstaafl.