It seems by rigour you mean something like “the ability for a theory to be a complete system without any sense of contradictions”

No, I mean rigour in the sense of being free from given assumptions, allowing reason to be fully self-grounding; this is the only possibility for philosophical science, as soon as you proclaim that reason is unavoidably conditioned by some given (as Marx does in the Afterword to the Second German Edition of Capital), you rule out the possibility of philosophical science and condemn philosophy to opinion. [explained further in lecture 1 here]

I mean rigour as it being grounded in assumptions derived directly from material experience and describing further the material world.

You can’t do philosophy in this way for the reason above and because you cannot derive from “material experience” that reason is conditioned by material experience, this is why empiricism isn’t philosophy.

Hegels system was more rigorous in the old sense of philosophical rigour, but Marxs was more in the sense of having some direct explanatory power and being able to be used to impact the world.

The notion of a philosophy of praxis violates what (scientific) philosophy (described above) is, Hegel goes over this in the Preface to the Philosophy of Right, Maker also does so in ch. 8 of Philosophy Without Foundations but you have to take that with a grain of salt due to the non-metaphysical reading (and also some “doctrine of ‘whatever’”-ism (Yibing, Back to Marx, p. xxi), but that doesn’t matter for the argument).

It seems your measurement of alienation is more roundabout than the one for commodity fetishist (how did we get from ‘degree to which alienation is felt’ to '[quantity] of proletariat?)

Because the objective historical inversion where dead labor rules over the living is the process by which the proletariat (a class of propertyless laborers) comes into being and becomes the absolute majority (“For [alienation] to become an ‘intolerable’ power, i.e. a power against which men make a revolution, it must necessarily have rendered the great mass of humanity ‘propertyless’, and produced, at the same time, the contradiction of an existing world of wealth and culture” (The German Ideology)). The degree to which alienation is felt/is is the degree to which a greater and greater amt of the population is rendered propertyless “cogs” in service of capital.

And lastly, it seems you think of the feelings as someone experience them might be primary, you keep using the word feeling to describe alienation. Is it the feeling which drives the proletariat to action? Or the objective conditions which lead to diverse reasonings to revolutionary potential?

For Marx, it’s the feeling which drives the proletariat to action, but it’s a feeling of “the objective conditions,” which also provide the proletariat with “revolutionary potential” in terms of making communism objectively possible (“material basis”).

“Looked at historically this inversion appears as the point of entry necessary in order to enforce, at the expense of the majority, the creation of wealth as such, i.e. the ruthless productive powers of social labour, which alone can form the material basis for a free human society” (Draft Ch.6 of Capital).

“this development of productive forces (which itself implies the actual empirical existence of men in their world-historical, instead of local, being) is an absolutely necessary practical premise [for the upheaval of alienation (communism)] because without it want is merely made general, and with destitution the struggle for necessities and all the old filthy business would necessarily be reproduced; and furthermore, because only with this universal development of productive forces is a universal intercourse between men established, which produces in all nations simultaneously the phenomenon of the ‘propertyless’ mass (universal competition), makes each nation dependent on the revolutions of the others, and finally has put world-historical, empirically universal individuals in place of local ones” (The German Ideology).

I think it’s important to emphasize the feelings side because, despite some things Marx and Engels have said (see “Four Letters by Engels on Historical Materialism”), within Marxism communism is not an inevitability mechanically resulting from the economic conditions of developed capitalism, the proletariat still must actualize their revolutionary potential to take hold of the immanent negativity within capitalism (i.e. there is a “subjective dimension”).