Arithmetic Circuits (ADDERS!)
As you say, there are a lot of references to Carry Look Ahead adder and Prefix adders,
such as the the Ladner-Fischer adder and Kogge-Stone adder.

How everywhere I looked, it seemed these were shown only as block diagrams.

But I finally found a real gate diagram here for a Kogge-Stone adder which might help you:



These is for a 8-bit adder, but you should be able to cut it to 4-bits easily.