I like what you say here.
When one does, lets say, Mahasi's insight method, what does one observe? One observes what arises in the present moment.
When one does Goenka's vipassana method, what does one observe? One observes the feelings that arise in the present moment in the body.
When one does "Samatha" Method of Ajahn Brahm, especially first two steps, what does one observe? One observes what arises in the present moment. When one reaches his super deep level, what does one observe? One observes the present moment so closely that one cannot think about it. Thoughts are always about what has just happened (even if split second ago), they are always at least split second after what they are supposed to observe.
So while certain technicalities of practice are different (label or be silently aware), (Sweep the body or observe it at entire body at a time), the effect seems to aim at the careful attention/observation of the present moment.
In fact, it seems that silent awareness of the present moment can go even deeper and more immediate than labeling because one is not distracted from present moment by paying attention to labels which always lag what they label, and thus focuses entirely on the present moment rather than commentary of it (even if it is one word).
"Life is a struggle. Life will throw curveballs at you, it will humble you, it will attempt to break you down. And just when you think things are starting to look up, life will smack you back down with ruthless indifference..."