Learn First, Then Daven
Time spent in Gemara and Tosafos clears the mind and prepares a person to pray.
The Yehudi did not treat Chassidus as a way around Torah study. He taught that learning Gemara together with the Tosafos purifies the mind and leaves a person fit for tefillah. The point is practical. A mind that has been stretched by a sharp question and a careful answer comes to the Shemoneh Esrei awake and orderly, and the words of davening can then carry real thought. This was the path of Peshischa: study and prayer joined, with the sharpness of learning feeding the warmth of the heart. Those who gathered around him were asked to bring both, and not to rely on feeling alone or on wonders.
Source: Tiferes HaYehudi (Kosov, 1912), p. 29, compiled by Baruch of Kasov.
Choose one morning this week and learn for ten minutes before you pray, even a single Gemara question or a halachah you have been meaning to study. Keep it slow and careful. Then, when you begin davening, see whether your mind is steadier and the words feel closer. If it helps, keep the same small habit for a month. You are not adding a burden, but giving your tefillah a clearer place to begin.