Since you're asking for warm-ups, not 'how to'...
I sing in half a dozen throat styles, especially syzgyt.
After studying Hefele a few years back, I moved on to analyzing the intervals I could achieve with vowels (caps are long): I-U II-i III-E IV-o V-A VI-O VII-a VIII-U and minors iii-e v-u vi-O.
With that you can do solfege warm-ups: DU Di DE Do DA DO Da DU... RU Ri RE Ro RA RO Ra RU... MU Mi ME Mo MA MO Ma MU...
You will find that most songs which stayed famous for decades have chords that match those vowels. I'm sure it was unconscious, but that's simply what sounded best, instrumental chords which matched vocal formant chords.
..and that was helpful for awhile but eventually I outgrew that as well.
[I was lately able to make good use of that repurposing it for a polytonal take on yodeling. yo Du LA HE HU = I bV V III(+oct) VIII. Practice dipthong howls to simplify things first.]
It's not quite like we can simply sing multiple notes. Rather it's like our vocal formants come complete with a standard instrumental overtone series, but we are capable of accentuating some harmonics and dampening others to sound more like multiple fundamental notes. The process is bi-directional. Anna-Maria uses vowel sounds as an entry-level means of accessing that harmonic accentuation/dampening, but the vowel formants are ultimately beside the point. The real point is acquiring total accentuation and dampening control of the harmonics. On a prepared guitar this can be done by attaching a miniscule weight (like a ring of brass wire) to the string, especially near the bridge - in just the same way as it's the high stuff in the mouth which can boost or choke the division-wavelengths of the larger wavelength (by being located in or out of phase with them). Technically we are adding 'Helmholz resonators' which both need to be located correctly, and have 'a' resonant frequency with the harmonic overtones we are accentuating (or make them non-resonant to kill frequencies).
You have roughly 35 registers you can be working in, five locations you can use as your vibrational source, and seven locations you can use as resonators. If you are lucky the five overlap and the seven overlap, but even then it takes practice or planning to know when in a song to change registers for the smoothest transition between them.
That said, these five vibrational registers, along the lines of chest-voice, falsetto, head, whistle are what a typical singer is going to warm up with (if even that). As a polytonal singer for each of those notes (which may well span five octaves if you've learned to use them all) one additionally has to consider the accompanying resonance spanning across the seven resonant chambers top to bottom. For any given note you can pick any second note as a resonant accompaniment. For every single vibrated note you can portamento through your entire range of resonators. For each of those notes, somewhere in that portamento range you will find octaves and fifths of that note which produce those signature syzgyt-sound harmonics intermodulations, those little buzzy rainbow spots, where your sine waves convert to triangle waves due to all the 'generated' harmonic content (as opposed to natural horn/windpipe harmonics).
And that is roughly my recommended exercise, to go through your scales, but, for each note, to additionally slide through the entire octaves of accompanying resonant notes, stopping at all the syzgyt hotspots you can find. With practice you will instantly recall where to find them.
Actually even that is rather tedious, though worth doing once or twice to start with. From there on out I would simply sing your favorite warmups (mine are Peer Gynt's Solvang's Song (in Marita Solberg opera style), Over the Rainbow, and Amazing Grace) but in a style in which your 2nd resonant frequency is like a 2nd bird in flight, swooping a graceful curvy flight-path behind the first (your vibrated tone), stopping for some syzgyt warbling on occasion.
Anna-Maria Hefele was the holy-grail for me just a year or two ago, but today upon a revisit I realized I've even outgrown her, as apparently she is limited to alternating between instrumental syzgyt style and lyrical vocals, while i have learned to do both at once (but not with all vowels; I have to sing some words with entirely wrong vowels). (Perhaps she can too, and simply doesn't for exactly that reason.)
Her voice isn't as rare as the internet makes it out to be. Traditional cowboy yodeling involves some throat singing, which now that I think on it, they probably picked up through contact with the Inuit. This is in turn has left a mark on some bluegrass folk vocal styles. Also many sweet voices naturally resonate unconsciously, though it tends to be in one interval like a fourth or sixth.
Lately I've been emulating synthesizers (even more lately, other vocalists). Anyhow, I also found it useful to sing into a free app pocket oscilloscope on my Amazon device to get my sine (strings) and triangle (horns) waveforms down perfect. Squares, like some arcade-sound synths, are terribly challenging, but can be somewhat reached. Back when I was just after note combos, a good spectrograph tuner was indispensable. Mine arranged the octave in a circle, further rings out for higher octaves - way useful to learn true full-range 'polytonal', as opposed to just throat of some variety.
I volunteer twice weekly in a small venue that plays a wide range of genres of world class musicians
(including Tuvan and Mongolian throat singing bands, one of which gave classes the afternoon before the show - which made an absolute world of difference over what I'd picked up on my own. It instantly unlocked doors and I was star pupil)
, three per night, and over the past year I have evolved to essentially being the backup if not lead singer for every single band playing. Because I typically hadn't met them till after the performance and was sneaking into the act as an unseen audience member, I learned to emulate all the instruments so I could start off just like a reverb extension of their music, totally transparent, then play it by ear to see how much latitude response I had from the band. Typically I'm thrown solos, if not having a delightful counterpoint jam. - Anyhow, the point there is practice practice practice. If you can fit in emulating any instruments in any genre, as polytonal as possible (when you get better, yes, you can actually start working in a third note) - you're golden.
My only gripe is that, while I sing basso-profundo to mezzo-soprano, F0 to F5, having been born male, my chest voice is a couple octaves lower than I'd like it to be, and I'm limited to emulating female vocalists with head voices (which is rarer for females, Marita Solberg for instance). There are a few exceptions I can emulate like Joan Baez, Bobbie Gentry, and Elizabeth Fraser, but still very few. I'm gaining ground here too though, just starting to touch on balancing multiple slightly-voiced lower vibrators, while still working in head voice, like Tori Amos. The more I keep at it, revisiting things which seemed hopeless earlier, the more I keep being able to do. I took to serious singing very late in life and hope it can last. I do find my voice giving out at shows increasingly, especially if it's cold and damp.
For my own shows I find i typically veer into musical vision quests, and end up channeling the music of several western native tribes.
Our local tribe of musicians in Bellingham, WA is actually fairly saturated in throat singers. I don't know if that's a national trend or we're just ahead of the game.
On a reread of your question, I see you are also looking for help even finding the magic spots. Memorize the ones you have found as references. If you can set them to a lyrical song, that will help. Most importantly, move around a lot, doing wauw-wauw-wauw's and reer-reer-reer's (all the vowels, really) all over the place. As with the bass stuff deep in your chest, all that crazy stuff in your mouth is on a sliding frequency spectrum (with some location gaps). Get a feel for sliding along that spectrum. While your bass resonance and treble resonance are in totally different locations, if your bass resonance moves higher, your treble resonance to find that sweet spot will need to move higher too (equally in pitch distance, but less so in physical distance). Think of it like a guitar fretboard, various notes plus n-frets higher in pitch. They are both logarithmic. An inch of travel near the heart is going to require a matching 1/4" of travel in the mouth, or along those lines anyhow.
Another hint that helped me a lot: Buy some good authentic Tuvan throat singing CDs and sing along with them in the car. It's like learning to sing to regular vocals. It helps to emulate a reference.
Anyhow, good luck to all of you angels joining the ranks and making music more alive, down to the vibrating soul of creation.