OK, I'll bite.

Settle for a smaller final image. Zoom less - you might be pushing your camera's minimum-focus distance with the zoom. Keep the shooting distance; aim for a final image about 1200px instead of the ~1700px you're getting. Your pics are a little out of focus at the edges; it might be a lens limitation which this suggestion will eliminate.
Stop down. f/2.5 results in a really shallow depth of field. A setting of around f/5.6 (in a point and shoot) or f/8-f/11 in a dSLR will increase depth of field. This will help make up for minor out-of-parallel between the lens and the coin. At f/2.5, you might not have enough depth of field to focus both devices and fields.
The above will require you to increase exposure time, as less light will be getting in. With a stiff camera mount and a delayed shutter, there's nothing stopping you from going down to 1/30 or even slower in the interest of getting enough light to the lens. I've shot nice exposures with full-second exposures, just to see if I could.

Just the aperture change I suggested would require you to go from 1/500 as you're shooting, to about 1/200 or so.
By "directly above," I assume you mean the light is as close to the lens as possible. Try two lights just like that, at 10:00 and 2:00, as close to the lens as possible while being above it. Going from three lights to two will require additional exposure, too; added to the narrower aperture you're probably looking at about 1/80-1/100 to get the same brightness on the shot.
Add a lens hood. Unless your entire shooting room is finished in matte black, including your body, you're getting at least a little light bouncing from various points and into the shot. This lowers contrast and adding a hood will help you play with lighting to reduce the areas of "darkness" such as at about 11:00 on the obverse pic.
Be prepared to use different settings for obverse and reverse. Differing percentages of fields/devices mean less/more light bouncing from the fields straight onto the lens. I vary exposure for Morgans a lot - all other things being equal, the reverse of a Morgan gets 1/200 when the obverse gets 1/125, for instance.