Not so sure about that statement. Has it been FAQ'd accordingly ?
If not , I'd say RAI he is to shut down all other enchantements when Glittering Robes ais used. Whether these enchantments had been taken before or after GR became "active" is imho irrelevant. As long as GR is active, no other enchantements can be active. Simple as that.
However, I suggest to send this question to GW clarification as it (stacking ) may have a significant impact...