Has it been working?

Hard to say; it's only been a single night for me. But I'm already tracking my sleep; and https://www.google.ca/search?q=blue.....t+screen+sleep offers more data than my personal experience, so there's reasonable hope.

Eeeenteresting.....

Depending on who you ask, you either need to cut out 'short-wave light' or 'blue light', so it's possible that instead of a red tint, I need something closer to an orange, amber, or brown tint. Fortunately, I also ordered some clip-on sunglasses. I suspect that you might already have a set of shooting glasses in the appropriate shade, if you want to give that a try yourself. :)

Clever, like the rat you are! May I take it that you still use caffeine for the opposite effect?

Kinda-sorta-maybe. It's astonishingly easy to become habituated to caffeine, which means that it only brings your alertness back up to what it would have been if you hadn't taken any in the first place. So I try to avoid having it regularly; but I do have some green tea on those occasions when I decide I /need/ to be more wakeful than I'm feeling. (And when I'm in the mood for a hot beverage, I've gotten a taste for caffeine-free "red tea" aka "rooibos".)

As someone who's been using f.lux for about a year, I would like to say that color shifting and reducing luminosity on your main screens does help with reducing "dancing lights" behind your eyelids when you go to bed, if that's something that prevents you from sleeping. If the last screen I look at is my non-color shifted 3DS, I get all sorts of lightshows when I close my eyes.

I'm not sure if I can attest to f.lux's actual affects on sleeping patterns, because I also started getting into soundscapes/low-frequency drones at the same time, which has definitely helped me sleep. An additional thing to try, if you respond well to audio!

> audio

Well, for some years now, I've been using a white-noise generator, in the form of an eight-inch desktop fan. (Actually, it's closer to brown noise.) Sometimes I'll throw on a classical or baroque music station before I hit the hay, but I haven't bothered looking into anything more complicated. Any suggestions on where I could start learning some of the basics you probably currently take for granted?

mynoise.net has a great selection of soundscapes and noise generators, including natural, industrial, and synthetic ones. Donating to the site is totally optional (the whole site's selection is available for free, except for the "really random" thematic generators and simultaneous loading, I think?) This is a great way to find your preferred background noise...you can even experiment with different colors of noise within a generator! A lot of soundscapes might not do anything for helping you wind down, but as a neat plus, some of the "bad for sleep" ones are great for getting inspiration for writing.
mynoise is also great because it has an app on the Apple store (no version for Android yet, iirc) so you can reduce the work an Apple smart device would do running a sound generator, both on the internet data and battery side of things. If you go this route, though, I recommend getting some kind of external speaker for your device, because sound clarity can be very bad coming from the tiny built-in ones. If you don't mind sleeping with earbuds, those would be even better.

Minimalist music can contain low-frequency drones, but you'll have to look out for which ones you respond to best. Youtube has 9 hour "meditation" or "sleep" videos, some that are more melodic than others. You can either listen to them for a half hour or so before bed or stream them while you sleep. For shorter tracks, there are some good minimalist musicians on Fur Affinity - Sage is my favorite.

All that said, a large part of using audio to help you sleep is psychological, I think...if you find something you responding to in a calming way, you can use it as part of a winding down playlist. When you're planning to sleep, run through some of that playlist. You might "tune it out" on a surface level, but it can play a big role in convincing your body to slow down.
(Personal anecdote about the psychological affects of drone music: a low frequency drone-heavy song I like came on when I was driving and I noticed I was losing focus, even though the song isn't part of my usual sleepy rotation.)

It sounds like you are desperate. I was there once myself, working a night shift and struggling to stay awake. Used to guzzle energy drinks; tried all the stuff that was out there. Fell asleep behind the wheel a few times and went off the road once. Started passing out while walking around the warehouse, blinking and finding myself someplace in the building with no idea how I had gotten there. Started having panic attacks and paranoia. I found out later that the reason I was so tired was because I had too much blue light getting in my room during the daytime, which interfered with my ability to get into deep sleep. At that point I had basically gone a year without any sort of restful sleep, and I was literally dying. Put up some light blocking curtains and my problems instantly vanished like magic.

So yeah, I know from firsthand experience that light exposure can fuck with your body's natural programmed cycles.