Thanks everyone! That really helped.
There were a few other things that I had to make sure of also.
Images placed in InDesign that were made in Photoshop or another program should be in ckmy format. The background needs to be in the same ckmy. Transparency blend must be set at CKMY, then Transparency Flattener presents must be set at Rasters/Vectors: 0 Line art and text resolution: 600, Gradient and mesh resoltuion 300. Exporting to PDF must be done under present PDF/X-4:2008 Compatibility: Acbrobat 7.