If I understand the diagram correctly, your "1b" is the right decomposition. All the tables in "1b" are in at least 5NF, though.
The notion that you can normalize to 2NF and no higher, or to 3NF and no higher, is a common misunderstanding of how normalization works. It's quite common to start with a relation that's in 1NF, and in a single step end up with all the relations in 5NF.