The two things that made the most immediate difference to how I felt in the water when I started with TI, were the relaxed neutral head and spearing the arms deeper to help get my hips up and achieve better body balance in the water - it was a epiphany to me..
Sometimes with TI, we encourage swimmers 'swing the pendulum' a bit too far to start with when making changeswhich is one of the causes of some people misunderstanding TI methodology - context is everything.
People who struggle with patient streamlined leading arms between the strokes I might encourage to be a little too patient to start with while learning to not think about simply "pulling" through the water and focus more on being streamlined.
The arm depth too is something some TI swimmers can 'overcook' a bit. Hand depth level with or just below the depth of the chest should be enough to give good neutral balance in the water and get the hips up if everything is nice and relaxed. Spearing too deep can make breathing a bit tricky sometimes and create a little too much drag.
I am a certified level 3.0 Total Immersion Swim Coach.