I had a customer's quilt once that she said she knew it was a mess but to quilt as best I could. It was a large star(can't remember name) that puckered up in the middle. I used fluffy batting and added a small amount of additional batting where the pucker was the worst. It came out pretty good and she was very happy at the way it turned out.
I used a large, swirly pantograph to quilt it.

Congrats on the finish! amazing pattern. Love Edyta!

Spray starch and a steam iron can take out a lot of slack. Good luck!

I think you should block it before you sandwich it, to quilt it. Soak in the bathtub w/ a mild soap or Synthrapol. Blot and roll up in a large beach towel. Spread out on a flat surface you can pin into. I use the back of my foam design wall, made from pink insulation boards. Or some use their carpet, but lay down a clean sheet first. Pin (use sturdy pins or T-pins) to keep it in place and pull if you need to to get those wrinkles out. Let air dry. You can aim a fan at it to speed the drying. When dry, then sandwich and quilt it. I block many of my quilts that are meant to hang on a wall after they are quilted, before squaring up and finishing the edges. This makes them lay flat on the wall.

I blocked a top that had too many waves in it to consider being able to quilt them out. I did the blocking method and it worked great. Ripples gone.

The quilts with the most ripples are usually the ones I hand quilt since I can put each section as I go along in the frame and it has a bit of the earlier section in the hoop when you reposition to a new area. My experience is that I ended up with little to no rippling by the time the quilt is finished.