When noting mental or emotional states, do it quickly, energetically and precisely so that the noting mind is continuous and powerful. Then thinking stops by itself.
Unless you can note the wandering thoughts, you are already defeated when attempting to concentrate the mind. If your mind is inclined to wander, it indicates that you are not really noting thoughts energetically enough. The acquired ability to do this is indispensable.
If you are aware of the content of thoughts, they will tend to go on. If you are aware of the thought itself, then thinking will cease.
Do not be attached to thinking and theory. Meditation is beyond time and space. So do not be caught up with thinking and theory. Insight will arise with deep concentration, but logical and philosophical thinking comes with shallow concentration.
Drowsiness can be overcome by putting in more effort. Labelling activities vigorously is helpful. Note sleepiness energetically, if you accept laziness, you will go on half asleep.
Actually, the energy to note is always there. The trouble is that you are reluctant to do it. The mental attitude is very important. So, do not be pessimistic. If you are optimistic, you offer yourself an opportunity. Then there is satisfaction in every situation and there will be less distraction.
A human being has a great variety of abilities and the strength to do many things. If you want to develop this meditation to its ultimate goal of complete awareness you will need to put a determined effort into the practice. If you put in this all out effort you will achieve the final liberation from habitual clinging, fear and confusion.