I've got some experience in this one- use quickplay or make a new career. The song you replaced will have it's score overwritten if you score higher on your custom song. For instance, I accidentally played Ride the Lightning in my normal (expert) career, and now I've got a 500+ thousand score in My Curse, which it replaced, which has an optimal score of 398,484. If I FC My Curse, it'll have gold stars and display the Ride the Lightning score.
So to save yourself this issue, play in a new career specifically for customs, or use an iso of a different region than your own, so it creates a new save file.
Or I suppose you could force it to make a new save, but I have no idea how to do that...