Can you post some new photos? What wattage rating is your iron?
For the MJE350s, your soldering iron is very unlikely to be able to heat them up enough to damage them. You need to see solder flow through the hole that the lead passes through and wick up a little bit on the other side. From the original photos you posted, there's no solder coming through on the other end. For the center lead of the MJE350, it takes a lot of heat to get this going, and without allowing that to happen, the flux inside the solder will create an insulating barrier between the solder joint at the lead of the MJE350. Once it is hot enough, that flux will be displaced and you will get a proper joint.
This is also consistent with the high voltage you are seeing, and I would bet that one LED on the 9 pin socket isn't glowing anymore either.
-PB