Late to the party but would like to chime in nontheless.
I sympathize with your frustration somewhat. This year I posted some of my songs (new and old) to youtube and distributed through Distrokid and the only "promotion" I ever did was to post my youtube links on my personal facebook with a couple of hundred friends, which resulted in likes from my mom and my sister, along with one occational comment now and then. Despite this my monthly listeners on Spotify grew every day up until it plateaued at 15k about a month ago and aggressively decreased after. Now it's probably down to single digits. The only reason for this was that Spotify had some of my tracks on their algorithmic playlists a little while.
I still don't know how and why they were selected for the algorithm, but I did learn that the algorithm is very powerful. I assume the same applies to other platforms, like Youtube e.g.
This made me do some research about promotion and learned about playlist pitching etc. I pitched to some user playlists that didn't require me to pay, resulting in one track added to one playlist, I don't think I've gotten a single play from that.
Youtube (and internet as a whole) has great resources about music promotion, but I find the VAST majority is aimed towards bands and aspiring pop stars. A lot of talk about social media presence, image, live gigs and such. I don't want to be a "brand", I would prefer to not even have my face associated with my music. All I'm concerned with is that the people who would enjoy my music could easily find it.
As for your complaint about Facebook groups, as people have pointed out, a lot of them want to inspire discussion and sharing knowlege in a particular field and don't want to be cluttered with self promotions. Also, have you actually looked at the groups that allow or encourage it? It's filled to the brink with posts with virtually no engagements from anyone. Mostly for the reason that people post the song they want to "promote" and then bounce. No one is interested in listening to the other contributors and most potential fans are generally not a members of those groups. I found the same results on sites like Reddit etc.
Before I went on my promotion research-binge, I also posted a link on this very forum, although not for the reasons of gaining listeners but for feedback to progress my craft. There is A LOT of people here with a wealth of knowledge. I didn't recieve any comments then either (not a diss towards this forum or any of it's members, I myself didn't listen and give feeback to other posts, so I'm just as guilty as anyone). If you're primarily looking to spread your music to fans I don't think this forum should be your main focus.
One tip I picked up was to do collaborations with others, for a chance to pick up some of their fans, but this could be hard if you've got no established connection to work with. In that case this forum (and others) could be a good starting point.
Also, covers of famous song could give your works great spread, but therein lies problems with permissions and costs. Besides, often when I see a Youtube channel with lots of popular and well recieved covers their occational original works usually recieves a tiny fraction of the same engagement. Generally, most people are there for the fun covers, not originals.
Another angle is doing related videos on Youtube, like tips and tutorials for mixing/orchestration/composing etc. But you risk running in to the same problem as above. If you're doing good tutorials and gain traction, then that's what people will be there for. I'm as guilty as anyone in that regard. If I follow a channel based on their sample walkthroughs/reviews, I tend to spend very little time diving into their original music.
Most of these hurdles dissappear however, if I'm primarily a fan of their music first. In that case I LOVE to watch anything they present about the process. The problem is to get people to first notice your music.
So, all in all, it's not an easy beat to dance to and I get your frustration. My best tip, by far, would be to try to "hack" the algorithms of varios platforms, but I have no good idea of how to do it.
I think I could do better on Youtube by video tagging (I do none of that) and adding descriptions describing the "point" and thought process of the pieces I upload. Most friends I explain that to really enjoy that and it often gives them a whole new level of appreciation of the music, but I believe it wouldn't have the same (maybe even opposite) effect on a stranger reading it on the internet. Besides, I'm the kind of dude who wants the listener to figure it out on their own.
Finally, watch out for scams, there are a lot of them. E.g. Don't pay some random dude to listen to your track with the promise that, if he likes it, he'll write about it in his blog or add it to his playlist. Check if anyone reads his blog or listen to his playlist, and don't pay him for merely listening. After he gets his money he has no incentive to feature you. Good marketing cost money, yes, but make sure they actually can deliver results.
And bevare of bots and bought "likes". It may look good on your socials (for a while) but most platforms see through that and can take actions against you.
TL;DR: Work the algorithms, do collaborations, do covers, present related content. None of them are easy and sure to bring any results, but they are more likely to work than posting in Facebook groups.
