I may be wrong, but is the OP suggesting that there is a shim between the cup and the lower headtube? If so, the shim may have been inserted simply to prevent the cup from rocking in an out-of-round head tube.

If this is so another shim made of an aluminum soda or beer can might be all that is needed to secure the new cup. This type of shimming was a common fix, that worked quite well, to manage a cup/frame interface that wasn't perfect.