Your critiques are good places to start critiquing Weber from I feel. They are very accessible and especially the protestant -> capitalism thing shows the idealism that Marx and half the Hegelians fought so hard against.

I also see a couple things that Weber did well (especially review stuff which became important for later for myself), but Marx did quite a bit work on culture in his works, not only in the German Ideology in which he describes some conceptions of how the mechanism between modes of productions and class as well as super structure is, but also in later works. I always wondered why people would skip over that when Capital contains so many great critiques of capitalist culture that are used to this day in anthropology frameworks in some way or the other.