No, iterating FCs in model builder is the only alternative approach I've had as well. You should be able to use the wildcard feature to limit classes it operates on, but yes it will check all candidates in a workspace.
If you're having problems with the field map, I recommend connecting an example class to the FC to FC tool in MB, setting your field map to your liking, the n connecting the iterator back to the tool. It will maintain the field map and apply it to the inputs from each iteration.
