This ground method is often used in low level audio amps to reduce hum. Your drawing shows the ground at the output stage, it should be at the input stage, probably right at the mic connector ground.
Fred
Fred brings up a very good point, one which I learned when my dad taught me to build my first audio amplifier, I was about six years old. It is interesting that a connection can be drawn from the way the schematic is drawn to the way the equipment is actually wired.
I learned to take a piece of solid #12 or #14 house wire, remove the insulation, and use that as a ground bus for all components grounded in all audio stages. I started with an insulated piece of wire, possibly extracted from a piece of romex. Squeeze the insulation in a vise, and it will peel off the wire and provide a nice clean section of copper to provide your ground bus. As Fred mentioned, connect this bus to the chassis only where the mic connector enters, this is the low-noise ground reference. Route the wire above the tube sockets, and support it at the far end with an insulated tie point. Ground all resistors, capacitors, etc, from each stage, to this ground bus. The alternative most folks use is to ground to the nearest chassis point, rather than use an independent ground bus. This is fine for RF, because the chassis provides a low impedance (at RF) reference point. But at audio, the chassis may have different AC potentials at different points, caused by fields induced from power transformers, or other devices nearby. The dedicated ground bus will minimize hum and noise in your audio stages. Also consider using twisted pairs of hookup wire to the heaters of each tube. The currents in each pair of wires will cancel, minimizing the hum radiation from the 6.3 volt AC heater currents. Many manufactures just ground one side of the heater circuit and connect each tube heater to chassis, thus requiring only one heater wire to each tube. This induces AC currents in the chassis which find their way into the low level stages, creating a hum that is impossible to suppress.
You mentioned the .25 uf 6SJ7 screen capacitor as a frequency killer. This capacitor is just a screen bypass, filtering the DC and decoupling any stray signals on the DC bus from the screen circuit. It will in no way affect the audio response of the amplifier stage, because it is not affecting the interstage coupling or bypassing (shunting) any high frequency audio components to ground. Capacitors in series with the signal path, or in parallel with the signal path and ground, will have an effect on frequency response and stage-to-stage phase shift.
By the way, the 6V6 is being operated in conventional "beam power tube" mode, it is not triode connected. The screen, or beam forming electrode, is connected to the supply at the B+ end of the output transformer. But, as you stated, the feedback to the previous stage will improve the frequency response, reduce distortion, and reduce the output impedance. How much effect this will have is determined by the amount of feedback. Often, the feedback is taken from the output side of the output transformer, but, in that case, care must be taken to make sure that the amplifier will be stable, and not oscillate, due to phase shift in the transformer at higher frequencies. Feedback from the plate of the output stage to the prior stage is relatively safe. Feedback around multiple stages gets more complicated due to cumulative phase shift in the interstage coupling circuits.