Want to replace the speakers in my work radio. Need some help between two choices.

Do you mean that the component side of the amplifier board faces the speakers and forms the rear wall of the speaker enclosure?
My girlfriend bought the same radio for garden use. She also ordered the Dayton DMA80's so I might as well open it up now. This is what the inside looks like. The rear half if completely taken up by electronics but as you can see in the second photo I can place plenty of damping material in the front half. And look at what it says on the speakers, CS JS78-122. This radio is brand new and these are the stock Creative speakers, just like in mine.
 

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Thanks, there doesn't appear to be much opportunity to apply damping in there!

The random surfaces presented by the componentry should help break up any major internal reflection modes.

If you must experiment, stick your foam only to any accessible plastic surfaces, and avoid covering the electronics.
 
I found a 12mm thick felt sheet in the back of a store room at work so I started experimenting after work. The first thing I did was I lined the speaker section with a thick bitumen tape. It's heavy and dense so it's perfect to absorb vibrations. I then placed the felt over it with spray on glue, closed everything up and did a test run. Even though the surface area to work with is small it makes lot of difference. As you can imagine a plastic casing will inevitably produce a hollow sound to some degree but that's mostly gone now. The sound is fuller and a bit warmer with this modification. This is pretty much all I can do with this radio but I'm completely satisfied now with the sound quality.