I found the solution in this discussion. R234 deserves the real credit for this.

Do note that for some reason, if I copy an instanced effect and edit any of the instances, it copies them, so I suggest copying the basic parent unusual effect before you instance it, then individually adjust each instance. It resulted in no problems for me, but your experience might be different.

In the parent particle, I removed the shower01 and shower02 children (the falling meteors), then either removed or unticked the Set Child control points from particle postion operator (this centers the ring to the control point instead of it being above.)

Then I did this in both unusual_meteor_cast_text_green and unusual_meteor_cast_wheel_green :

In render_animated_sprites , change orientation control point from -1 to 0. (this allows rotation via control point 0), and disable the Rotation Spin Roll operator (it makes the particle effect spin on their own. You can also change spin_rate_degrees to make it rotate in a different speed or even direction.)
If you want to disable the fadein effect at the start, Alpha Fade in Random affects that, and you can adjust the size in Radius Random

I love what you did with the particles. How do you do it? I can't seem to rotate the ring when I tried it out.