The truth about LED's used with AC power is very simple and too many folks read way too much into it.
In order to light an LED up all you really need is an LED & a resistor. Simply solder the resistor to the PLUS (+) side of the LED and the negative (-) side to the ground. In other words hook up the positive (+) to the center rail and the negative (-) to the outer rail. That's it nothing more nothing less.
For most LED's you will need a 1K ohm or larger for the positive (+) side.
Of course if you don't want them to flicker (fade out) you will need to use a bridge rectifier and capacitor of certain sizes but that is another story for another day.
Dave, LBR
P.S. - If you require LED's we probably have what you want at a VERY reasonable price with shipping in CONUS included. Special orders do not bother us we just want to serve the hobby. Give us a try I don't think you will be sorry you did