With that story out of the way, what methods exist, if they even exist, to reduce this perceived loss? Hedging?
Yes, there is a method, it's called trading perfectly - if you buy exactly at the bottom and sell exactly at the top, you won't have any perceived or real losses. But no one trades perfectly, so some perceived losses are inevitable. You can either try to improve at trading to reduce them, or just accept them as a part of the game.
Also, you can continuously sell during the bull market and then continuously buy during bear market - this way you will be guaranteed the average value of the cycle instead of relying on your trading skill. This is probably a good idea for those who are absolutely bad at trading.