Great points!   I'm working on this lyrics first thing with the idea the lyrics should "exist" and are there to experiment with singing them as the melody and music get readied.  Since as you say it's a triangle, my thoughts are that even if the lyrics are there as a starting point, I can then update them (lengthen or shorten lines, add more or take away lines) as the song starts to take shape musically and the melody starts to dictate what needs to happen.
 
Writing the lyrics first, as you say, I think allows for the freedom to concentrate on the lyrics at the start.
 
For me presently, it's not as much as about which method or part of the triangle is best to start, or maybe they are all done as a stream of conscious creation together at the start as you just experiment around with ideas popping up.  Instead for me it's about my personal lack of discipline, or actually, lack of lyric output.
 
I'm making a choice (presently) to say if I want to work on a song, first I have to have lyrics.  This in my current self-discipline rule.  If I want to make some music at a particular moment, I'm forcing myself to say "have you coughed up the lyrics yet?"  If you have the lyrics, go ahead, go crazy on the music.  But if you (meaning I) don't have the lyrics for that piece yet, go back to your perch and write the lyrics on a notepad before showing up at the music station.
 
I know it's mean, but someone has to be the disciplinarian.
 
 

I might borrow that! Like I said above, I do find it much easier to write lyrics around a melody so that could be sort of my version of the 'same' method. I think it'd be handy to adapt the "one approach" method to my own writing style.
 
I write a fair amount of instrumental-only stuff and starting with a well-defined, well-thought out melody would help me out a lot with fleshing out a good arrangement.

After setting forth with my self discipline of "lyrics first" I've got updates to this concept from my using it.

1. Come up with the lyrics - while figuring out the melody and basic chords / song structure at the same time. Or snippets of each, and then work them to work together until the song structure (with lyrics) is complete.

I did write some lyrics first, entirely by themselves, but have found the stream of conscious method of lyric writing while checking if it works with a melody and chords is much more efficient and tight to a song usefulness. I ended up rewriting most of my "lyrics only" lines to fit music as I tested them out.

So in essence, jot down the lyrics like it's been done for ages. But the key for me is to "finish the lyrics" before getting into action on the song details.

2. I've confirmed and validated with my creative behavior that it's an excellent policy to not allow myself to go down the Sonar rabbit hole of wonderfulness unless I arrive at the gate with song structure and lyrics ready to sing on. Previously I didn't have this requirement and I had many more songs than lyrics as a result. After a while trying out this commitment I now have singable lyrics for each song I'm presently working. That's progress!

Sometimes I write lyrics and then when I start recording,  the melody dictates a lyrical change. So I am using a hybrid method I suppose, start with a melody and find some nice lyrics to fill the notes. If I have no lyrics and music,  I will start mumbling words out with melody until I suddenly fall upon some lyrics, this method works well for me also. Just remember melody is so important so don't be afraid to change it a few times until you hit on something you really love.  Years ago I would come up with a melody and would not change it because I thought it was the best I could do. However,  over the years of writing and collaborating, I have become much better at excepting change as a great thing to try.
I guess we just keep learning !
Mark