Hi Ed. In addition to the API(s), there's a specific Freebase<->Wikidata mapping dump which is a little old (18 months), but very compact and easy to work with. The identifiers are likely to be pretty stable, so if the entities you are interested in have been around for a while, it might be easier to work with.
The three hits for your sample topic make me suspicious about the quality of the mapping though
I don't know if this dump was used as the basis for the identifiers loaded into Wikidata, but you might want to consider building in some safeguards like double checking that names match -- whatever lookup scheme you decide to use.
Tom