I don't follow. On-screen banding doesn't matter as long as your color separations are right for print. Just viewing a PNG is no adequate test. Create a print PDF and check the separations in Acrobat. Still, even then there may be some banding and/or your color will become full solid. That background is just difficult to print
Your computer monitor is a single fixed array of red, green, and blue pixels that light up. In no way do they correspond to the four separate grids of much smaller halftone dots that will be created in print and rotated to different angles to form rosettes. So the banding you see on screen (in any program) is not representative of and does not correspond to the banding you will see in print.
If you don't yet have experience sufficient to judge the likelihood of banding being a problem by the numbers, the only way you can reasonably anticipate what will occur on press is to have the printing house generate a contract proof before committing to press.
It is usually a non-issue, assuming the normal commerical resolution imagesetting of offset printing.