Thank you for jumping into this discussion Atanu
You asked for questions:
1. Are we saying that people of the lower (working) varnas are less advanced spiritually (thamasic guna predominates) than those of the Brahmin varna (stavic guna predominates)? And that the reincarnation process incarnates them in the varna that is best for them?
You are always welcome, George
My answer is "Not exactly".
It is said that we are eternally free pure awareness. But Varna (the veil) hides that reality and binds us, as if, in cycles of cause and effect.
The Varna that we land into is our own doing .... due to combination of mental nature and acts.
Dharmic-religious prescriptions are supposed to be designed for removal of the veil.
A brahmin may be furthest from moksha because his duties may be difficult to adhere to. A brahmin cannot harbour desire or lust and should work only for welfare of all, generally as a teacher/priest. OTOH, a so called lowly Shudra may be very near to Moksha, because his duties have no potential for mistake.
But again, in present day, much of this is not relevant for two reasons. Very few people are actually acting as per scriptural requirements. And, it is said that simple act of surrender is the easiest way.