The resistors check OK, but they seem to run pretty hot. Maybe I should take a closer look at the resistance....
Wonder what would be involved in converting the reader to LED? Seems a small regulator on each reader board might do the trick.
The voltage is AC and the bulbs are in series, each dropping 5 volts. But now you have to figure out how to wire the LED's in series
rectify the voltage and reduce it . All things considered you may find it easier to modify the wiring and use the 5 volt reader
cards. I have to wonder about the bulbs on your shelf though, if they are all 14 volt bulbs then 50 volts would not light
them up correctly (probably dim). I would need to see the data sheets for those bulbs so that you can see how much voltage
is being dropped across the resistor.
Just as an FYI, the reel reader tester that I built uses 50 volts DC, the bulbs don't care about anything other than voltage.