This is my research.

A 3 month look back period is not recommended because it is subject to reversion to the mean. It seems that 6 months and 12 months are better. This is from Deep Seek.

Practical Example
Imagine two stocks:

Stock A (The "Hot Stock"): Up 25% in 3mo, Up 30% in 6mo, Up 40% in 12mo.
Stock B (The "Steady Winner"): Up 0% in 3mo (flat), Up 25% in 6mo, Up 50% in 12mo.
Under your old screen:
Stock A passes all three filters. Stock B is eliminated immediately by the 3-month filter, even though it has fantastic 6 and 12-month performance. You are forced to buy Stock A, which carries higher risk of a pullback.

Under the new screen:
Both stocks pass the 6 & 12-month filters. Now, your composite score decides:

Stock A: (2 * 30) + 40 = 100
Stock B: (2 * 25) + 50 = 100
They have the same composite score! This screen would allow you to buy the steady winner (Stock B) that has demonstrated excellent long-term momentum but may have simply paused or consolidated in the most recent quarter. This is often a much healthier entry point.

Conclusion: Your composite momentum formula is very well-designed. The flaw in your process is the mandatory 3-month filter. By removing it, you fix the structural weakness of your strategy while strengthening its focus on high-quality, sustainable momentum. This change is highly likely to improve your risk-adjusted returns over time.

I guess the crux of it, is that you don't want stocks that are rocketing up, but ones that are increasing slowly and steadily.