Not impossible at all, nor is it a scam. I've flown first class with NH/JL/SQ a dozen times the last few years and have half a dozen more F flights with NH/BA/EK (ok so BA first maybe doesn't count lol) coming up in 2023 - all using points. Have to do your homework. NH in particular is a tricky one post-reopening - there is unprecedented demand for flights to/from Japan right now following years of major hurt on the airlines' bottom lines, so you're joining the game at a rough time and trying to work with a particularly difficult program as NH is doing their very best to pull cash bookings as much possible currently.

EDIT: I remember this thread now - you have zero flexibility in your travel dates which also complicates your situation on top of everything else - flexibility is a bit of a must in the current conditions. As CPHflyer mentioned, you should probably widen your net to other options including SQ's LAX-NRT flight, which tends to be my fallback when NH options aren't doable.