Good question, I like the thinking but I don't have an answer either. Even if filtering restored it exactly as expected, you'd still have degradation to deal with. Separating the solution and freezing half might give similar results. One freeze-thaw cycle will cause some damage, but I'm not sure how that compares to the vial staying reconstituted for 12-16 weeks. Someone probably has charts showing purity after reconstitution versus after a single freeze.
Bacteria can grow in reconstituted vials over time, so I'm wondering if anyone has facts or opinions about filtering a vial that's already been mixed and used for about 8 weeks. Would that step limit additional bacterial growth? For reference I have a 100 mg vial reconstituted with bacteriostatic water but I'm only drawing less than 3 mg per week, and I'd like to know if filtering it again could safely extend how long the vial stays usable.