> Why you know the amp can run without the field coils?
What Sluckey said.
We know "from experience" (too many years of looking at everything) that the DC power in a field coil is "similar" to the audio watts that the speaker is rated for.(*)
One 6L6 can do 9 Watts (6 to 13 depending). So 4.5 Watts per speaker.
And a 6L6 with 2.5K load will probably be working near 250V 75mA.
4.5 Watts in 15K Ohms is 260 Volts 17mA.
The voltage is a good match.
Two 17mA coils will not pass the 75mA of the 6L6.
So we see the most likely connection is a 250V-300V 110mA high-voltage supply, with 6L6 and FCs in parallel.
And if we remove the FCs, the "under-load" on the high-volt supply is very slight. 110mA, 75mA, probably works the same, just a little more voltage, which the 6L6 can stand.
This is different from the typical radio. They ran a 350V raw high-voltage, dropped 100V in the FC wired series with the output tube run at 250V. If you remove the FC, no power gets to the rest of the radio. So a speaker replacement also means doing something to replace the filtering and dropping action of the series field-coil.
The third way to power a FC is with a separate DC supply. This is how they did it in movie theaters. The speaker was on stage, the amplifiers were far back and up in the projector booth. Long wires to carry the DC from booth to stage were more expensive than a DC power supply next to the speaker, plugged-in on the stage or screen-wall.
(*)There is no "magic reason" for this. The DC power in a FC is all about copper loss. We could reduce the loss with a larger wire size. But that makes the coil larger, increasing the average length of turn, so for the same turns we need a longer length of wire, and more resistance. The loss does fall as coil size increases, but not quickly; meanwhile copper is expensive. Also the larger coil means a larger iron structure which leaks more magnetisim, so we need even more turns.
I have a feeling that FC DC power runs 0.5 to 2 times the speaker rated audio power. Less FC power is lower midrange efficiency but also lower cost. Mass-produced table radios went this way. A PA amplifier needs maximum output, FC power is about as good as final-tube power, so they tended to use higher FC power. In a large movie-theater with 1930s tubes, efficiency was more precious than copper wire, so very high FC powers were used.