I generally prefer to look at the worst outcomes rather than average or median. Better for surprises to be happy than sad.

Your sessions with Chatgpt sounds like you pretty well covered all bases. Much more exhaustive than my timing test with spreadsheets & GTR1 values. But I found the same conclusion -- there is a wide range of parameters that work pretty well. Never forgetting that what worked absolutely best in the past was tuned for that past and likely won't be best in the future.

For this simple momentum screen I finally settled on a simple timing method that is just a small difference from what I already have automated.
Sell when the current S&P500 drops 1% below the 52 week SMA. Buy when it rises above the SMA. There needs to be a slight difference so that you don't get whiplash when it is right at the crossover point. 4% below works better with other screens, but in such a high volatility screen like this, 4% is too wide; you want to be quicker.

The BIG thing this timing did was in the 5 years 2/1/2000 to 2/1/2005. Where none of the other timings did nearly as well.
Untimed was -8.4% CAGR with -66% MaxDD.
Timed was +14.4% with -18% MaxDD.

That's the difference between jumping out the window and downgrading restaurant dining to McDonald's.