Block the quilt.
Lots of tutorials out on the web.
Here is one to get you started.
https://leahday.com/pages/how-to-block-a-quilt
I would be very hesitant to take steam to it with a poly batting.
Edited to add, it is very common for lone star quilts to volcano up in the middle. It is the nature of the beast. Some volcano as much as a "b" cup bra. I strongly suspect the quilt was problematic before you did any quilting.