In reading what you wrote and the testing you did, I would have to guess that the problem is in one of three areas. It is unlikely that all the servos in all the skulls have all suddenly gone bad at once. Your LEDs are working when run alone, so that suggests that they are OK, the wiring going to them are OK, and the relay board you are using is OK.
That leaves a ground problem in your wiring, the power supply itself, or the SSC-32 card.
Having one bad servo can draw down the power supply and cause these problems, but since you said that the problem persists even when you take each skull out of the circuit one at a time, I would have to say that is not the issue.
The easiest thing to do is check the easiest things first, then move on. First, use a voltmeter to check the output of your power supply to be sure it is giving you the proper voltage. Even if it does, that does not mean that your power supply isn't the problem, but if the voltage is wrong, then it most likely IS the problem. Confirm the voltage and then move on. Remember that the SSC-32 board power should never be less than 6VDC. The voltage going into the SSC-32 on the VL connector must be between 6 and 9 volts. The board runs on 5VDC, but it uses a voltage regulator on the board to convert whatever you put in down to 5VDC. The regulator itself uses up about 1 volt of power, so if you fed it 5VDC, the components on the board would only get 4VDC and could very well exhibit odd and erratic behavior. Be sure that has at least 6VDC. The VS input can be anything from 4.8VDC to 6VDC. That is what powers the servos.
The second easiest thing to check is your wiring.
Using a meter to check continuity and your eyes to look for physical issues, check the entire path of your power wires. Check every solder connection, check every screw connection on the SSC-32 board. Turn the board over and check the solder connections that hold the screw terminals to the board. They frequently develop cracks due to stress from over-tightening, or motion from the wires pulling on the terminal blocks. I have removed the screw terminals from more than one SSC-32 board and soldered the wires into the board directly to solve that very problem. It could be a break in a wire, an intermittent break, so move your wires around while testing, or a high resistance connection. It would be connected, but it's a poor connection, and it is dropping voltage across the high resistance caused by the bad connection.
Another way to solve a bad ground problem is to run a new ground wire. Don't remove the old one. Just get a new wire, connect it directly to the negative from the power supply, and run it to the SSC-32. Bypass the screw terminal and solder it directly to the board on the back side where the negative from the screw terminal goes in.
Before we move on, I need to know how you wired your extensions.
I usually only run the signal wires out through the extensions and I run a separate set of thicker wires out for power to the servos. That allows me to run fewer wires. Just two wires go out for power and get split out to individual servos at the skull end, and then one wire per servo for control as opposed to three wires for each servo. If you do wire it that way, you still have to connect the ground from the power supply that is driving the servos to the ground on the SSC-32 board from the VS input. Otherwise you can get erratic behavior.
If all your wiring checks out and running new grounds and new positive wires along side your old ones does not solve the issue, it's time to start swapping out parts.
The first thing to swap out is the power supply. Just because it is reading the correct voltage at the output doesn't mean it is not still the problem. It could be that the power supply is no longer providing the current that it should, or it's characteristics may be changing when under load. Replace it with a different power supply and give it a run.
I also couldn't see from your picture if you are using two separate power supplies or just one on the SSC-32 board. I know you are using the 12v for some of the lights through the relays, but that's not the part I am questioning. What are you using to power the VL input? Is that separate from what you are using to power the VS input? Unless it is a 6VDC power supply, they should be two separate things. As I mentioned, the VL input should be between 6VDC and 9VDC. the VS input can be as low as 4.8VDC but not higher than 6VDC or you will start burning up servos, or shortening their life. If you are running both off the same 5VDC output from the computer power supply you are using, that could be your problem, and you have just been lucky up to this point. The VL input (Which stands for Voltage to Logic, or the chips on the board) Requires no less than 6VDC. For a test, run it off a 9V battery and make sure the jumpers are set correctly so that the VL and VS are NOT sharing the same input. You want the VL=VS jumper removed when using two separate power supplies.
See if that solves your problem running the SSC-32 with a 9V battery and the jumper removed. Use the power supply you have for VS. If you still are having the issue, then swap out the power supply, leaving the 9V batter in place on the VL input.
After that, if the problem persists, you may need to swap the SSC-32 board. It may have developed an issue. They are making different ones now that take a USB input directly. No need for a USB to Serial adapter. If you want to swap apples for apples, I have an old-style SSC-32 board I can send you as fast as you want it if you don't mind paying for shipping.
If you are still having issues, or you are not following along with these instructions and need help, call me at 603-646-3556. I will attempt to talk you through it.
