to the pins that connect to the chassis
Is this one of the type of tube designs which uses chassis as part of the circuit reference (aka circuit ground) instead of having separate wiring?
I see pin 10 on the RCA diagram shows as connected to the circuit, it did not jump out to me right away that pin 10 was also the chassis connection.
It is also interesting that the manual has much more discussion of unbalanced connections than balanced; were unbalanced connections so common in the 1940 and 1950 eras? I would have thought that with transformer coupling being so common that proper balanced transformer connections would be the default.
grounding 1 would make it even quieter? Floating is better than balanced?
Floating means no connection to the local circuit. The copy of the RCA manual I found has in the input wiring section a note that "Whenever a balanced source is used, remove the ground lead from the input transformer primary (terminal 1 or 2)." No mention of pin 7, so connecting pin 7 of the transformer does not seem to be a common or recommended connection.
With a transformer, "balanced" and "floating" are often the same, the input winding connects with only two connections to the source device, which may also be a transformer winding on an output transformer on the source device.
That may not apply if phantom power is in use, since that could involve a DC connection to the center tap from the phantom power supply (with later designs which supported phantom power). Not always, you could still capacitor couple into the transformer and use two resistors to the phantom power supply like is done on solid state preamp designs.
This design pre-dates phantom power since microphones would all have been either passive or tube in that time frame, so I would not count on the transformer being wound in a way that it could tolerate DC current through the windings, so resistors and coupling capacitors would probably be the recommended method unless you verified that the windings were such that the DC current through each half of the winding canceled and did not push the transformer into saturation.