Easy, replace Ca(OH)2 with NaOH.
That's the baseline anyways. That'd be conceding defeat. Not yet.
Maybe from a Chemist's viewpoint this sounds silly? "If NaOH works why not use it?" The motivation is more "applied"; costs might be a major saving. Even if the yields are a bit lower I might be able to accept that, factoring in the cheaper cost of Ca(OH)2 / more profitability in isolating and selling CaCl2 as opposed to NaCl.
Your result is about what I was expecting. I think the insolubility of the calcium salts is basically the source of your problems.
Not all of them. CaCl2 is very soluble like Borek indicated. Maybe if I can get purer Ca(OH)2 or add lesser of it there should't be as much left over insoluble Ca(OH)2 to form the emulsion? The Chemistry seems a success; an emulsion might have Physical solutions. I'm not sure but optimistic.
Add HCl to make CaCl2 and separate.
That's an idea I like. Will try right away. Thanks!