You can try this. Try opening the eps directly in Ill. Set eyedropper tool to only pick up fill (double click tool to open settings window). Use it to select one color and drag it to swatches pallette and convert to cmyk spot. Repeat as necessary. Once you have colors, try using the magic wand to pick a color and then fill
Or, In Photoshop (converted to cmyk), use magic wand to select one color. Write down the cmyk values to create a new swatch in Ill. Then create a path and export path to Illustrator. Fill the path with appropriate spot. Repeat as necessary. Reassemble the whole thing. The good part here ia that it gets you out of rasters and into vectors, lessening any resizing problems and giving crisper edges and better transparency..
Or, in cmyk Photoshop, use magic wand to select a color, and note values. Select a color with magic wand and select similar (select menu) if necessary to select non contiguous area with same color. You can use channels pallette to make that a spot channel. When you get the fill color window, create the cmyk color that you pickled up with eyedropper, Repeat as necessary. Create clipping paths for any areas that require transparency and save as eps.