You've described your jig for turning the pendants 'off-centre' but I can't quite visualise the whole thing.
Here it is. Firstly I put a spindle in a chuck and turn one end, then part it off thick enough for a pendant. Next I have a sacrifical piece of wood mounted in a chuck, and it has a dished shape cut into it so that the side of the pendant that I've finished sits into the 'dish' with a little double sided to hold it in place.
I always bring the tail-stock center up whilst I clean up the edge and the outer rim of the face, then slide the tail-stock away and finish off.
Next comes the fun bit....my quartered block of oak that I so badly explained earlier on ( why didn't I just take a photo?)
The groove around the outside is for a chunky rubber band, but for now it's got a bit of garden plastic-coated wire in it to hold the 4 pieces together.
I slip the pendant into the hole, front face outwards and rotated so that the grain lies nicely, then tighten the chuck, start up the lathe and drill the hole for the leather thong. Then I usually turn a little dished cove shape around the edge of the hole.
When the pendant is reversed, it has to be rotated until the hole is central, which is easily achieved by bringing the drill bit back up to the chuck and rotating the pendant until the hole and the drill line up together, tighten the chuck jaws and clean up the back of the pendant, adding a few details (as you suggested.
Voila....there you have it....a double-sided pendant....
Les