Water dries skin -- removes skin oils -- regardless.

High chlorine (FC > 25% of CYA) leaves my skin feeling 'dry' and 'tight', so that might be what you were experiencing. But I don't think everyone's skin is the same in that regard.

Many people report that their skin feels 'less dry' when they begin using salt (NaCl > 2000 ppm) or borates (> 60 ppm). Some people have added salt, just for the feel. Again, their 'dry' skin may not be the same thing you are experiencing. Regardless, I'd try borates first. Salt does increase corrosion, and I'm not sure it's worth it, if you don't have a SWCG.

The saponification (oil => soap) of oils *is* affected by pH, but I don't know if the the difference between 7.4 and 7.8 or 8.0 would be enough to notice. However, it surely won't hurt to lower your pH and see.