I agree with what you're saying that it's cyclical but at the same time, the very best teams don't tend to stay down too long and some teams that are 'up-and-coming' never truly get over the hump.
The difference is usually good management vs bad management. Knowing when to 'go for it' and when to hold back usually separates the good ones from the bad ones.
Out of the teams you listed, I believe you are right with New Jersey though they'll have to proceed carefully and build it the right way without trying to take shortcuts. Los Angeles looked a lot better when Alex Turcotte was supposed to be a top notch prospect. The jury is still out on Byfield as well but if neither pan out, that's going to hurt their chances going forward.
As far as Ottawa goes, I just don't think Dorion is a good enough manager to get it done. They'll end up a good team though for sure at some point but probably not a true contender. I think Mr. "The Rebuild is over" is going to find a way to f*** it up.
Lastly, the NYR's core is probably older than ours. Apart from Fox, Shesterkin and the 2 "Top-2" wingers they got in recent drafts, they are severely lacking in the young center department. Panarin is 30, Zibanejad is 29, Kreider is 31. If they sign Kadri as rumored, that's not going to add to getting younger.
I would add Detroit to the list as I think they've done a good job since Yzerman took over. You can tell he's not going to rush it and he's going to build that team the right way.