My workflow was pretty simple:
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Open the image in an editing program, such as Photoshop or GIMP.
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Verify the image is in Grayscale mode. Some scans in PNG format are saved as bitmaps with a 1-bit color depth, particularly those scanned by Google. These images will have a black line added at the bottom edge when imported in Illustrator or Inkscape, or when uploaded to the Glowforge app. To prevent this, the images need to be converted to Grayscale, which has an 8-bit color depth. GIMP will automatically convert these images, no extra steps needed. In Photoshop, go to Image->Mode->Grayscale, leave the Size Ratio as 1 in the popup window and click OK.
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Crop the image as desired.
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Clean up any stray black pixels in the image. There may be easier ways to do this, but I just used the Brush tool to paint any unwanted pixels white. (To check the cleanup, you can Invert the image to easily spot the remaining stray pixels, then undo the Invert and continue cleanup. Photoshop: Image->Adjustments->Invert, GIMP: Colors->Invert.)
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Rotate the image if necessary. I rotated the images so the majority of straight lines ran horizontally, parallel to the motion of the Glowforge head. This seemed to give a cleaner result when engraving closely spaced parallel lines.
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Resize the image. I resized these images to be 3.5" in their longest dimension, to fit on the 4" coasters.
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Posterize the image using 4 levels. Photoshop: Image->Adjustments->Posterize, GIMP: Colors->Posterize. This is done to be sure the white image areas stayed solid white during resizing, and also helps sharpen the image. This could be done with other tools which would give more control, but I found Posterize did an acceptable job in this case.
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Export the image as a PNG. Photoshop: File->Export->Quick Export as PNG or File->Export->Export As…, GIMP: File->Export As…
After processing the images, I created a file in Illustrator with a 20" x 12" artboard and used the Rectangle tool to create 4" squares. The processed images were then centered inside the 4" squares. In the Glowforge, the squares were used to cut a cardboard template to help with positioning, then the coasters were placed and engraved. I used the settings listed by @Jules in the Settings for Engraving on Slate thread as a starting point, and tweaked them slightly by lowering power by 1, which seemed to give a slightly cleaner engrave. I also used “Vary power” in the GRAYSCALE option instead of “Convert to dots”. If the image comes out too light, just run the engrave again without moving anything. I had to run the engrave on the coaster with the clarinet twice, and I was impressed with how accurate the second pass was, even after the head had been parked.