Barb,
Presuming you took the advice to be sure that send image data is set to all in the graphics tab of the print dialog, I think the issue may be with the RIP, although it is a bit troubling that the banding is being displayed with 32-bit color.
Someone, I believe it was Gerald, has posted a number of times about how some RIPs treat vector and raster data differently which can result in color shifts during transparency flattening. I think the same thing may be at play withthe banding. How are the gradients produced? have you considered, if it is possible, creating them as images in Photoshop?
Perhaps this, from the help files, is useful, too:
Improving gradients and color blends in print
PostScript Level 2 and PostScript 3 output devices can print up to 256 shades of gray, and most PostScript desktop laser printers are capable of printing approximately 32 to 64 shades, depending on the device resolution, specified screen frequency, and halftoning method. Banding occurs when each available shade covers an area large enough for you to see individual shades. Also, if you specify a gradient using two percentage values that differ by less than 50%, youre specifying a narrow range of shades thats more likely to result in banding. If you have difficulty printing smooth gradients without banding, try these techniques:
Use a gradient that changes at least 50% between two or more process color components.
Specify lighter colors, or shorten the length of dark gradients. Banding is most likely to occur between very dark colors and white.
Increase the percentage of change in the gradient.
Decrease the screen frequency for the document (PostScript output devices only).
If banding occurs in an imported graphic, such as an Adobe Illustrator file, you might need to adjust the original graphic.
Print to a PostScript 3 output device, which is capable of producing smoother gradients.
Use shorter gradients. The optimum length depends on the colors in the gradient, but try to keep gradients shorter than 7.5 inches.
Peter