It is worth appreciating how peaky the current pulse is going through the two diodes, and how short a duration it is - especially when a large filter capacitance is being charged. The current peak can be easily 5-10x the 'AC' peak current for a similar output load power, and so has a significant impact on the transformer secondary winding voltage drop at that time - which would be 'flat-topping' the ac waveform fed to the AC heaters.
The distortion in the AC voltage may also cause some error in your ac voltage measurement, depending on how good a true rms reading your meter can make.
With respect to the DC heater voltage and hum, those particular heaters will not now see 6.3Vac pushing leakage current across the heater-cathode interface, but rather the low AC ripple voltage level. To my mind, there is no net benefit in trying to reduce the ripple from 100mV down to 1mV, as both of those levels are hugely below the incumbent 6.3Vac. And there is an adverse affect in adding more and more filter capacitance - the diode current pulse peak value gets higher and the duration of the pulse gets shorter - that means the stray harmonics are pushed higher up in frequency and so are more likely to become audible elsewhere.
The AC powered heaters are 'grounded' in that schematic, as the voltage of each AC winding terminal is bounded as it floats from near 0V ground to near ~7-8V as it is pushed from one level to the other as the diodes conduct in one direction and then the other. The valves using AC power may then exhibit higher hum levels than if they were grounded by a humdinger, as the voltage swing (relative to ground) is about twice.
You can use schottky diodes to lower the diode voltage drop during conduction, and hence raise the DC voltage available for those heaters. And some designers purposefully lower the heater voltage on input valves to reduce other forms of noise - if that is at all measureable.
The distortion in the AC voltage may also cause some error in your ac voltage measurement, depending on how good a true rms reading your meter can make.
With respect to the DC heater voltage and hum, those particular heaters will not now see 6.3Vac pushing leakage current across the heater-cathode interface, but rather the low AC ripple voltage level. To my mind, there is no net benefit in trying to reduce the ripple from 100mV down to 1mV, as both of those levels are hugely below the incumbent 6.3Vac. And there is an adverse affect in adding more and more filter capacitance - the diode current pulse peak value gets higher and the duration of the pulse gets shorter - that means the stray harmonics are pushed higher up in frequency and so are more likely to become audible elsewhere.
The AC powered heaters are 'grounded' in that schematic, as the voltage of each AC winding terminal is bounded as it floats from near 0V ground to near ~7-8V as it is pushed from one level to the other as the diodes conduct in one direction and then the other. The valves using AC power may then exhibit higher hum levels than if they were grounded by a humdinger, as the voltage swing (relative to ground) is about twice.
You can use schottky diodes to lower the diode voltage drop during conduction, and hence raise the DC voltage available for those heaters. And some designers purposefully lower the heater voltage on input valves to reduce other forms of noise - if that is at all measureable.