Reducing acidity without creating "soapy" taste
I use Calcium hydroxide, (pickling lime, Cal, slaked lime), to raise the pH of my tomato sauces. It does not take much, and you don't get that nasty flavor that comes with using sodium bicarbonate. You can find the stuff in the canning aisle in a U.S. grocery store. Mexican and Asian stores  also usually carry it. The Latinos use Cal to nixtamalize corn prior to making tortillas. An eighth teaspoon, or 0.2g, is usually enough for 250ml  (a medium can) of tomato sauce. You'll have to play with that number a little. I've tried several different bases to neutralize the acid they add to tomato sauce. Only Calcium hydroxide seems to have no down side.
If you are adding the right amount of finely powdered CaOH, you shouldn't have to wash it out, as it will turn into Ca citrate, or some other soluble salt. You may well be using too much. The reaction does take time, so 10 min or more waiting is not unreasonable.