So you prefer to read it as they cannot stack with anything not listed as something they can be worn with. Fine.
I, on the other hand, am reading that they stack with other armour, but restrict which armours they can be worn with. And as you should know, worn armour takes up the "body" magic item slot, whether the armour itself is magical. Mage Armour and Bracers of Armour (and other similar effects) do not take up that slot, but still provide an armour bonus. They are not a "certain type of armour", they are a non-armour effect that gives an armour bonus. Since you have an armour bonus, and nothing that is disallowed in your body slot, you can wear and stack the chahar-aina and dastana. My reasoning for this is that they did not word them to only function with certain armours, which you think they worded it as, but rather stated separately (yes, in the same sentence) that they stack with other armour, but limit what they can be worn with. If this were not so, why would they use roughly triple the space to say "...can only be worn with and stack with padded, leather, or chain shirt armour"? The fact is they didn't, because they can be stacked with other armour bonuses that are not actual worn armours.