[Arran]

What about paralleling the filament of the pilot lamp with part of that dropping resistor you need for the tube heaters, that was what they used to do in AC/DC sets with a plug in ballast. Then you could use an ordinary 6.3 volt pilot bulb of some sort. I'm still not sure about the durability of a mini a stand alone 120V LED, even the Christmas light strings have them connected in a series parallel arrangement. Unfortunately the diode trick doesn't cut the 120 volts in half it comes out closer to 80 volts rather then 60 volts if I remember correctly, they have a calculator posted on a British site for figuring filament droppers out.
Regards
Arran