I did some various versions and tweaks to try out some of the ideas here and some I had already.
First, I removed the internal “root glow” from the last one. There was a kind of glowy ball at the bottom but I think it aliases the rest of the textures oddly and is probably better done as a non-axis aligned billboard separately. Anyway… so these are all just flames and no internal bottom highlight.
More analysis after video…
[video]http://www.youtube.com/watch?v=rOpS5ifEyTo&feature=youtu.be[/video]
So, it was important to me to confirm that the multi quads thing was not a silver bullet. Even my own conventional wisdom kept trying to steer me in this direction. In fact, I was so paranoid about the “billboard effect” that I originally indexed into the texture atlas based on view direction so that the textures would change as you walked around the flame… but the flames are already cycling through the atlas so fast that you couldn’t even tell.
…indeed, to my eye, I can pretend that the star ones are also billboards and I don’t have any problem fooling myself until the edge-on artifacts show up… and that’s hardly a “good thing”. These artifacts could be removed with some clever alpha application based on view direction, etc… but then it would look just like the billboarded one. 
Also, the multi-quad versions have a significant downside for me in that I have to turn off depth writing. For batched geometry that is a significant down side.
You can also see that from the top, the star shaped ones look like a monkey’s behind. Covering that up is going to be significant. One thing that’s really nice about Mythruna’s current bubbly flames (based on round particles) is that they look good and 3D from all angles. So I don’t want to take too many steps back.
Finally, given the idea of trying multiple different effects (like an ember in the middle or whatever) I tried seeing what it would look like to combine two separate flames: a normal sized outer one using the lower intensity blending and a smaller inner one using the original internal additive blending. This one shows a lot of promise for the cost of just one more quad.
I may also try to add a “poof” particle flame where single flame rises from the bottom to the top as a single particle. I think it would create some nice variation and can help round out the top views also.
Anyway, I still need to make my own flame texture atlas and (for my purposes) make the whole effect look more like an illustration/painting and less photographic.