“I’ve heard of tzaddikim who davened Shachris even after Chatzos.”
I’ve heard of people who redefine the work “tzadik” to include people to violate the halachah.
5ish: You realize that the poskim specifically addressed the issue of having to chose between kavanah and zman hatefillah. The halachah according to everyone was always that zman hatefillah takes precedence, until the Chassidim chose to ignore this.
For a lot of the year, zman hatefilla is as late at 11 o’clock. If you can’t focus by that point in the day, you need to see a doctor.