My opinion would be create a new queue option that players can choose to use. Random Partial. you get put in any LFR you can join, and its a partial but you also get something along the lines of a Satchel of Exotic Mysteries for doing so.
Problem this solves, it does not force people who want to join a fresh instance to do a potentially already failing partial instance. It also puts people who want to do the partial instances, in a partial instance, for instance people who just want their valor.
Blizzard should really think their bandaid solutions through, because this just creates a cascading problem of I join partial, i kill remaining boss, i join fresh i kill unlooted bosses, and leave creating another partial.