We know Leopold wasn't amenable to the partitions, but what about Josef? Leopold has a connection to Spain (Spanish mother and wife, while his sister was queen of Spain). Josef has no such connections (or if he does, they're more distant), plus he's got that whole thing going down in Hungary.
Alternatively, the partition of Italy that was reached at Utrecht/Rastatt/Baden satisfied France and Austria (but not Spain). Could they not do a similar handshake deal - France gets Tuscany-Parma/Naples, while Austria gets Naples/Tuscany-Parma? Milan was imperial territory so I don't think its going anywhere. Spain, plus the Southern Netherlands and the Colonies, gets a Habsburg king in exchange for France getting an Italian secundogeniture in either Florence or Naples. Maybe we can even pull off the series of Franco-Austrian marriages (if only in part) planned at the time: Élisabeth Charlotte d'Orléans won't be marrying Josef I or Adelaide of Savoy to Karl VI, but Anjou can wed Maria Elisabeth or Maria Magdalene of Austria and Karl VI can marry Luisa Maria of Savoy. A sort of early diplomatic revolution, as it were. It won't keep the peace any more than OTL, but if Austria and France are "allied" then random hangers on like the dukes of Lorraine and Savoy will just have to suck it.