Rather than use a NUD4001 which has a fairly limited power dissipation and needs to be on a pcb in order to get rid of heat effectively it's quite easy to use an LM317 which can be heatsinked easily. The voltage variation is easily taken care of with this method.Thanks for that great info AAH.
I did find this link to the NUD4001 data sheet. On it there is an example using two of the NUD4001 for a dome light application. But that dome light application is using a single LED and thus, a high watt resistor, which I don't really want to do - it doesn't apply to my LEDs.
So could I just use figure 6 for the dome light situation, putting 3 LEDs in series and a lower wattage resistor like you mention above? For each of the small boards I received from the group buy from years ago, I could make one of these (with 3 LEDS wired in per board) for each of his shelves and run 12v to each one to give lighting useful for him to find his tools in the dark.