After all this discussion I decided to tackle the three switch stands with blown leds today. I ruined the first trying to unsolder the wires from the copper strips, but succeeded on the last two. I sure couldn't make a living from it, but nice to know it's possible. And, I have spares now.
You can just pull the LED out with the wires attached and then solder to the LED, no other soldering required. I just slid the plastic gear and metal inside brace down to expose enough wire to attach the new LED. All four went like clockwork, it gets easier once you do a few. 
I'd still like to know why they're dying...
I did the last one that way. I just need practice, hopefully on other lights than them. The instructions I was going by said to supply 4.5 volts to test them. Isn't that a lot for a white led?
That's a lot, or ok it you put a 1K resistor in series with your test leads.
That is what is coming out of the switch with the stand off. I don't see any resistor after that. I have a switch off the layout. I'll check the voltage on that one.
No. The voltage without the load (switch stand) will not be the same as what it is with a working switch stand installed. The series resistor is on the circuit board in the switch.
And do not test without a resistor in series. It only takes a small wrong higher voltage without a series resistor to burn out the LED.
I used 3 volts when I tested my repairs. But 4.5 volts is what you get with the switch stand not connected. I was worried I needed some higher voltage led. I just used a regular 3mm that I had from ledswitch.com. Hopefully they will work when the next one fails.
I never test LED's without a current limiting resistor. The current knee after you reach the operating voltage of an LED is VERY sharp, a couple of tenths of a volt will double the current.
