How can I tell if I am overdriving the amp or the speakers?

I am really sad to say it is my ears! Some of the music I listen to in the morning sounds good and sounds sharper in the evening. Same everything, Equipment, tunes and volume. If I keep it simple, like Bill Evans Trio or Art Pepper it is as bad, but the more instruments the worse it gets.

You've probably arrived at that certain age when you must pay the price for your extravagant volume habit. Surprised you hear anything but tinnitus.

Look at the Stereophile review of the Kef Reference 5 (2017). Go to measurements and look at first graph, the impedance curve is the solid line. 1k - 5k they appear easy to drive. I would try reducing the 4' distance from speaker to side wall, if there are walls, to 3' for starters. How far to the back wall ?  Hope this helps, Best.

In my opinion there is nothing wrong with your gear or your ears. The fundamentals of the alto sax and electric guitars do not go much above 1K hz. The piano obviously does but in most songs the range usually does not go much above 2.5K hz. So the harshness you are hearing is probably in the harmonics, which are being reproduced by the tweeter in your KEF's which also happens to be the frequency range the ear is most sensitive to. (3K-4K). 

Tone control is one way of dealing with the issue or if you are averse to that, room treatments would be the way to go or possibly a combination of the two.

As far as the music sounding better in the morning, it could be because there is usually more ambient noise during the day, which could help mask some of the higher harmonics. Is it possible that you are listening more critically in the evening and using the music as more of a background during the day?

My condo neighbors always let me know, so I bought a house

hth