(1a) I read books more than magazines. — correct
"More" in (1a) modifies "read".
(1b) I read books more than I do/did magazines. — correct
Since (1b) exists, then "than" in (1a) is the conjunction.
This conjunction in (1a) joins the clause "I read books more" and the clause "magazines" together.
(2a) I read more books than magazines. — correct
"More" in (2a) modifies "books".
(2b) I read more books than I do/did magazines. — incorrect
Since (2b) does not exist, then "than" in (2a) is the preposition.
The prepositional phrase "than magazines" in (2a) modifies "more" (although it seems strange to me).
Could you show me please all mistakes I did in my parsing?