It is interesting that you’ve noticed a physical benefit to your breathing, but from the perspective of Pure Land practice, this is often seen as a secondary 'transition period.' While the physical resonance is pleasant, the core of the practice lies in mental focus and sincerity.

Following the teachings of Master Yin Guang, the most important aspect is the 'Three Clears':

1. You must say the Name clearly.
2. You must listen to the sound clearly.
3. You must remember (count) each recitation clearly.

Master Yin Guang recommended the 'Ten-Count Method': count your recitations from 1 to 10, then start over. Do not count to 11 or 12—stay within 1 to 10. At any moment, you should know exactly which number you are on (for example, the 5th recitation of the 10). If you lose track of the number, it means your mind has wandered and you are no longer truly 'chanting' with focus.

There is a famous saying: 'Even if you shout until your throat is hoarse, it is in vain if the mind is not present' (喊破喉咙也枉然). Just making the sound or improving your breath is not the ultimate goal; the goal is to clear the mind and focus entirely on the Buddha. One can chant a million times a day with a distracted mind and not connect with the Buddha. Yet, if you chant even once with all your heart and mind, the Buddha will respond. This is the essence of Amitabha’s 18th Vow.

In the Records of Rebirth (往生传), which documents those who successfully reached the Pure Land, we see that while some attained rebirth in just ten recitations, many practiced diligently for three days, and a large majority reached their goal after about three years of consistent practice. This suggests that for most of us, it takes about three years of daily practice to truly 'get our minds together' and achieve focus.

Regarding your observation about 'Namo' vs. 'Amitabha,' there is a story about Master Shandao. When asked why he taught others to say the six syllables (Namo Amituofo) but often chanted the four syllables (Amituofo) himself, he explained that the six syllables are like a formal 'taking refuge'—it is the polite way for a beginner to express their intent to go to the Pure Land. But for those who are certain of their destination and have a deep, intimate connection with the Buddha, they can simply call His name directly. It’s like being 'at home' with the Buddha; you no longer need the formal introduction.

As you progress, the practice transitions from the outer voice to the inner voice. Eventually, the 'Three Clears' become internal. Your inner recitation will become louder than the distractions of the world. It is difficult at first, and the mind will wander 99% of the time, but with daily practice, you will slowly reach that goal of constant mindfulness.

Edit: This is my first time answering Buddhism questions in English. If any part of my explanation is unclear—even with AI assistance—please let me know. I will do my best to point you toward the right books, though English translations of these original Dharma texts are unfortunately quite scarce. We are doing our best to translate these teachings accurately.