“first trading day of any month” test is excellent.

Strategy Avg Start CAGR Worst
Mom 1 timed 28.0% 3.8%
Mom 5 timed 18.2% 6.4%

Interesting.
I recall reading that the best day was the last trading day of the month, because that's when active mutual funds dump their dogs and buy the stocks that have recently gone up, to doctor up their holdings so that they can say "See, we own the recent hot stocks and don't own any recent dogs."

Don't know if this is true or not.

Google is all over the place on this topic.

But regardless, when running a portfolio like this where you are selling and buying at the same time, I wonder if the day-of-month really matters.

I used to run my screens after the close on the last Friday of the month, so I had the entire weekend to run the screens and then do the trades on Monday. Some trade sessions were 4 weeks apart and some were 5 weeks apart.

A few years ago when I reduced the number of screens I run, I switched to run the screens after close on the next-last day and the do the trades on the last DOM.

My screen count has increased, so maybe I'll do some one way and some the other way.