If possible, one finds a new printer who can handle your files properly and doesn't insist on .eps.
What format are you delivering to the Printer? If it's anything other than PDF (and that's at their request) all the more reason to reread the first sentence. Why on earth are you moving things from Illustrator to Photoshop and back to Illustrator? Either one of those will save as .eps (ugh), though you need to use a clipping path for transparent areas coming out of photoshop (don't really know how Illy handles it when you say to save .eps with transparent background), but you are FAR better off with either native .AI or .PSD, both of which support transparencey, unlike .eps.If yo are delivering PDF, as you should be, it makes no difference to the printer what format the placed content uses (and it shouldn't matter to him even with native files unless he's hopelessly stuck in the 90s).
In any event, when importing from Illustrator, make sure to show the import options and check the transparent background box.
With all due respect to your “print shop,” their advice is at best lousy!
EPS is a “legacy” file format best reserved for graphical content from the 1990s and or for use with QuarkXPress.
Let's forget Photoshop for the time being.
If you are creating content in Adobe Illustrator and want to place that into Adobe InDesign, your best bet is to save the Illustrator document as a PDF file using the PDF/X-4 options. This preserves color managment and live transparency yielding the best results when placed into an InDesign document.
Perhaps you can explain better why or when you are going in and out of Photoshop with content from Illustrator, but EPS is never the solution in any part of this workflow.
First off, my print shop says that placed images should be in EPS forma
They should immediately become your former print shop.
Clearly, I need to more fully understand what my printer's requirements are. I see now that something isn't right there. Thanks for everyone's thoughts.