what exactly is the "result" you have issue with? cloudy calcium loaded naptha layer?
as long as the naptha is actually seperating from the solution this can still work. pretend the calcium clouding is not there and syphon it all off as normal. but then, add vinegar or ideally hydrochloric acid to your naptha and shake to dissolve all the calcium hydroxide, this part you can control though, adding only just enough acid to react with the calcium you can leave most of the spice in solution. Now you will want to base it again from scratch using sodium carbonate. this will cause even worse clouding than last time, however calcium carbonate should settle easily, and if it doesnt, heat and chill a few times and it should.
Also, before you do anything, try putting it in the freezer until ice only just begins to form, dont let it actually freeze over, then let it warm to room temp, then freezer again, try this a few times, freezer or fridge, colder is better. when warmed calcium hydroxide will dissolve a little. when then chilled, there is precipitation however, it will prefer to crystalize on existing particles, making them get bigger, and heavier, and more likely to settle. this works for certain hydroxides like magnesium, iron and manganese, as well as some basic salts too with similar properties so it should hopefully help calcium.
Going from ice cold to room temp is the same as going room temp to hot as far as crystal formation goes, things always dissolve when getting warmer, precipitate (if saturated) when going colder.