It sounds like you have addressed two of the most common causes of brown leaf tips, which are over/underwatering and using fluoridated water. Other causes that come to mind are fertilizer, sunlight, and humidity:
Fertilizer: Too much fertilizer can cause soluble salts to build up, resulting in brown leaf tips. Green flowers are also a sign of overfertilizing. It sounds like you haven’t fed the plant recently, though, so this shouldn’t be the cause.
Sunlight: Is the plant sitting in direct sunlight for most of the day? Too much intense sun can burn the leaves and cause brown tips. Peace lilies like bright light, but they don’t like direct sunlight for extended periods. An eastern windowsill would be the ideal spot to keep the plant, as it offers bright morning sunlight but isn’t exposed to the intense mid-day sun.
Humidity: Peace lilies appreciate some humidity, so if it gets too dry in your home, leaf tips may brown. Combat this by placing the plant on a tray of moist pebbles or near a humidifier.
It sounds like you have addressed two of the most common causes of brown leaf tips, which are over/underwatering and using fluoridated water. Other causes that come to mind are fertilizer, sunlight, and humidity: