Coin Experiment

The ledge won't be a problem. In fact, its' rough surface might allow air to circulate underneath the coins, and minimize your need to flip them regularly.

I strongly agree that the coins should be flipped regularly, to tone them evenly.

The environmental chemistry of the air and sunlight above would be very different to the paint, dust, temporary high humidity and lack of sunlight below the coins.

I've done this many, many times. Your results will vary pending on so many things.
1. If you have the window open.
2. Temperature and humidity of air if window is open
3. Placing coins on raw, new wood
4. Placing coins on old, varnished wood
5. Window facing N, S, E or W.
6. Amount of sundlight making contact with the coins. Not that the Sun will make a difference, but in the Sun, the temperature goes up.
7. Window in what room. A kitchen window where lots of cooking is done makes a real difference.
From your photo I'd guess your coins are on a inside, closed window. Yet all the other factors I mentioned are still of concern.