I have an idea how you could make thin FIMO balls with an almosti-spherical interior cavity. Well, I didn't invent the technique, it's was originaly used to mold jewelry :
Lost-wax casting
What you do is quite simple :
1- Find a candle and carve yourself a few spheres out of wax. If the wax is too hard, soften it by putting it in hot tap water (which should be around 50C) for 1-2 min. You can then shape them simply using your fingers.
2- Put the shaped wax spheres in the freezer for 10-20min to re-harden them.
3- Using the wax beads as an interior mold, apply a thin layer of FIMO over them.
4- Puncture the FIMO-wax sphere using a small nail or big needle.
5- Cook your FIMO normally on a baking sheet. Orient the balls so that the puncture hole points downward.
The wax should drain out during cooking, leaving you with a thin small fimo ping-pong ball ;-). Now you only have to drill that puncture hole to the desired LED size. These thin balls should absorb less light yet still diffuse the light nicely.