I'm hoping that you are adding an acid to your pale beers, but it does appear that your results with your amber beers agree with the somewhat low alkalinity of your tap water. However, that tap water may not have enough alkalinity to keep the mashing wort pH from dropping too low. Adding the baking soda should be the surest way of increasing mash alkalinity. I'm hoping that you are only adding that baking soda to the mashing water and not the sparging water!
As you note, baking soda does add sodium. But I've found that low levels of sodium seem to enhance the flavor of dark styles. However, if the flavor is not to your liking, then using pickling lime might be a better option for you. The problem with lime is that its purity is not constant and it eventually turns into chalk when moist air is allowed into the lime container. So, you might have to add a bit more lime than calculated to achieve your targeted mashing pH. That is kind of a sucky reality, but it might be worth it if your beer tastes better to you. I guess my warning about lime purity is just to prepare you to add a bit more lime if your pH's end up too low.
Keep working at it. Remember, my advice is only a starting point. You still have to refine that advice to fit your brewing, your beers, and your taste preferences.
BN Army // 13th Mountain Division 