Missed this:
> Looking at secondary AC voltages (hot to hot) might get messy if the unit is earthed.
Yes, and usually not necessary. Plate and heater windings are usually CT to ground: read each side. For 2-diode DC, the higher AC voltage dominates (though they should be exactly the same). For heater, or 230V motors, add the two 3.2V readings for 6.4V (or 2*115V=230V). If the heater CT is 2*100 ohms, that causes insignificant error against a 10+Meg meter. If there is no heater CT, the meter may ground one side without harm.
Yes, there are reasons to float. I think my 230V well-pump was once connected to two 115V points so that it got.... zero V. Obviously that was not right, so they moved wires until it ran (and never corrected the fusebox markings). For across-the-line work like that, you can use a dumb passive meter, or the DMM cuz it's cheaper today. The VTVM was never the universal meter, nor an electrician's tool, it was the audio/radio workbench meter.
Reading low on most ranges: very low power supply (perhaps the PS cap is shot and it is limping on raw rectified ripple instead of smooth DC), very weak twin-triode, or sick meter. Meters usually work or not, though a 1940 meter may just have a weak magnet.
Check meter: in small print it may say "FS=200uA" or similar. Figure a resistor and 9V battery to make that much current (assume meter resistance is zero, near-enuff). Free the wires from the movement and run your test current through it; does it read full-scale +/-5%?