OK, that's about right for the line voltage you are getting. The 5998 is just pulling that voltage down quite a bit, probably just below the threshold of sufficient emission. My hunch is that to get the tube to work you would need to increase the AC mains voltage to the amp by 3%, about 7 volts. The easiest way to do this is with a variac.
You might also reflow all of the solder joints from pins B7 and B8 back to the power transformer. Just a little bit of added resistance from a cold solder joint could affect the heater voltage. For example, an added .1ohm of resistance from a cold joint with the 2.4A current draw of the 5998 heater could drop the heater voltage .24V. It may or may not help, but it's something simple to try. Also clean the tube pins really well.