Any juice reduces the amount of chlorine dioxide in the mixture. Fortunately chlorite seems to be the compound that helps, so it is not all that important how much the chlorine dioxide is reduced.
One way to avoid the taste is to limit the reduction on pH. The current protocol ends up with a chlorous acid solution with a pH of around 3.0. If you use less acid and target a pH of 5.0 you will avoid any taste issues.
The problem is that when you target a pH of 5.0 the activation time increases to around 24 hours. If you plan ahead you can avoid the adverse taste, but it takes some planning on your part.