I think DC is the only PI person in here, but if there are others lemme give you my reasons why I think you should do a secondary (if not LR) and a Note.
First, journals in a certain subject matter portray to the employer your interest in the subject is real enough to assume journal responsibility. For instance, I was gunning for environmental PI so I did CJEL. This rule especially applies if you snag executive board as a 3L.
Second, writing a Note sucks, but you need to do it and it needs to be not-terrible. I received two offers from PI orgs, and at both callbacks I spent at lot of time in the interviews talking about and fielding questions about my note. When writing a Note, be strategic with the topic and thesis. For instance, my Note was about standing in judicial review actions of environmental matters. My thesis was that, due to the unique factual and legal mechanisms in environmental law, standing requirements should be slightly relaxed in judicial review of environmental matters. My Note was directly applicable to the exact organizations I was gunning for, so they ate it up.
Third, on the subject of a Note, it's not incredibly hard to get your Note published in your secondary. So long as you write something well researched and not terribly written, then it's already better than half of your peer's Notes who are going to a firm and are just writing a Note to fulfill the requirement (plus the Note gets your major writing out of the way and creates a connection with a professor who could serve as a clerkship LOR!). Even if your Note isn't being published, you can still put it on your resume in order to spur conversation on it in interviews.
Disclaimer: writing a good note is tough. A good note will require about 4 to 5 hours of research a week for at least a month. It'll then take about 36 hours to compile your research and write it up. I probably spent another 20 hours of editing and addressing critiques from my Note advisor. Overall, budget at least 50 to 60 hours to research, 36 to writing, and 20 to editing. However, if you start early (I began researching in late August of 2L) and pace yourself, then it's not very stressful