Just about the worst thing you can do to a Jade is to keep it wet, but it seems you know this. I wonder about a few tings though. Just to make sure, the pot does have ample drainage holes, right? Even if it does is the bottom of the pot flat? I once had a house plant in a flat bottomed pot and, despite using a decent bonsai type mix, the drainage hole plugged up and caused problems. This happened because the pot had no feet so when I watered the fines could not be flushed away and eventually impeded drainage greatly.
Next, if the pot is excessively large the soil may be staying wet too long. That brings us to the soil itself, are you using a conventional type potting soil? If so, that in combination with either, or both, of the things I mentioned above could be contributing to your problem.
I know it's counter-intuitive, because of the shriveled leaves, but it could still be over watered sometimes if roots are damaged the plant cannot take up water and appears to be under watered. Result, a well meaning grower waters more making the problem worse.
Try this, get a chopstick or kitchen skewer and push it into the soil and leave it there. When you think it is time to water pull the skewer out and check it for moisture. If it is still damp don't water.