Perhaps better to look at the Heater circuit as a separate entity from the rest of the amp. The heaters are powered by a separate secondary winding from the power transformer (or, maybe a separate winding for the tubes in each channel). And, while the center tap of that heater winding is referenced to circuit ground for a couple of reasons, if you want to measure the AC Heater Voltage, you will need to measure across the entire winding; if you use circuit ground for one meter lead, you will only be measuring from the center-tap to one end of the winding, which will give you only ~ half of the total Voltage you are looking for.
If the Heater connections on a given tube are pins 2 & 7, for instance, one meter lead will go on pin 2 and the other lead on pin 7, with the meter set to AC Volts. Since you are expecting ~ 6.3 - 6.4 VAC, the meter range should be set to something higher than that, if it is not an auto-ranging meter.
Again, I would expect the Voltages to be somewhat higher than specified due to an increase in line Voltage delivered to your home, as compared to when the amp was new. Tubes were usually designed to operate well within + or - 15% or so of nominal line Voltage, since it could vary quite a lot from town to country and place to place back in the day.
What will be interesting to see is what Voltages you are able to read if the amp is acting up; they may tell you something more about what is going on. BTW, if you haven't heard it already, it is always a good idea to keep one hand in your pocket while measuring Voltages. This usually means that at least one of your meter leads will need to be clipped into place. This is to minimize the possibility that you would accidentally shock yourself up one arm and down the other.