My advice would be to follow the NCEES topic outline. As broad as some of those topics are, I would not skip or short-cut anything.
Even though the CERM is pretty large, I would suggest going through all of the topics (even if it's just skimming on the basic stuff) just to refresh yourself on things you may have forgotten, especially since you never know what NCEES will ask on the test. I would not suggest going through "Background Support", it would be a waste of time in my opinion because you won't be tested on that stuff.
What depth are you taking? That will affect how much time you put into each topic. I thought the CERM structural material is pretty good especially for the AM exam, and like I said, follow the NCEES outline - don't skip anything. They won't ask you to design welded members or reinforced concrete beams on the AM exam, but they will on the PM exam.
The construction material in the CERM falls short IMHO. I have the 11th edition and all it touches is construction earthwork, staking and layout, building and materials testing (minimal at best), and construction and jobsite safety (again minimal at best). There is also a management section that contains economic analysis, which I thought is pretty good but I took the construction depth and bought an engineering economics book that I thought was better when all was said and done. The CERM also "covers" budgets and scheduling. For AM study, I think the scheduling section is OK. Budgets and estimating fall way short though. There are different estimating methods that I'm sure a lot of people on this board can get into if you'd like, but the CERM does not cover this and those methods are utilized on both the AM and PM construction exams. Additionally, there are other books out there that cover construction topics into the detail needed for the exam that the CERM does not get into. Temporary structures is another topic missed in the CERM; although for the AM, the structures sections should suffice. I guess in my summary for construction, I would suggest investing in some other references regardless if you're studying for AM or PM. It seems like a lot of people underestimate how broad the topic is, even on the AM section.
Like you said, you don't want to miss anything - so I would go through all of NCEES topics and all of the CERM sections that apply. Probably not exactly what you wanted to hear, but once you've gone through the CERM and studied the topics, I think you should be acquainted with it enough to be able to flip to a specific section or page in the CERM without even looking at a tab or index during practice exams, sample problems, actual exam etc... - that's not to say you won't need tabs, my point is you should be as familiar as possible with the CERM.
Hope this helps, if you have any questions with different construction references, I'd be happy to list what I used.