The schematic is online here:
http://techpreservation.dyndns.org/s...ics/Zenith.htm
You'll need to get the DjVu plug-in or IRFANVIEW with its DjVu plug-in to open it.
http://www.celartem.com/en/download/djvu.asp
No need to add a resistor - the tubes will take the extra voltage from a silicon rectifier just fine (though some radios need a bit more caution... battery / AC ones especially)