[Chas]

This is what I would look at... before I pull what little hair I have left out

Be sure the tubes are correct, no substitutions, shields in place. Be sure none of the tubes have heater/cathode leakage and no gas.

Check the resistances in the string that controls the bias and that the potentiometer for volume is the correct taper. That can be done by using a VOM and dialing the pot up/down.

The volume potentiometer track may be worn...

Monitor the voltage at the pot as it is turned up down and does it have sudden jumps. Montor again at the source of the screen voltage for changes during a run up/down.

Those changes would indicate a failing dropping resistor upstream..

RCA use a punched tab for ground points in the chassis, but there may be other riveted ground points. The plating will oxidize over time and the riveted or possibly screwed connections to the chassis will fail at RF. Meaning a DC check of a ground connection is not conclusive.  Find a way to re-solder the tab grounds and solder the rivet grounds using an active flux, iron with a large bolt or drilling out the rivet and replace with hardware and star washer(s).

I have "discovered" that old dogbone and some later carbon resistors though may measure correctly with a VOM, change value as current flows, this is troublesome in radios that do not use an AVC as the problem manifests itself as loss of sensitivity as the radio warms or an abnormal increase in volume/sensitivity.

The clue is to monitor the various B+ and confirm the symptom as a voltage or current change. Measure across an added (5%) resistor the voltage drop. An other tool is freeze spray or an application specific heat gun...

If the tube sockets seem unreliable a cleaning method that does not remove metal is to take a dud tube and thoroughly sandpaper the pins with very coarse paper to leave them rough. Plug this tube in/out as may times as practical and the roughness will scrub the socket contacts at the best point of contact.

For this type of radio, a good earth ground and an external antenna of 25 to 50 feet may be helpful. One should not rely on the power source or the electrical system ground for set grounding.

Though the alignment method of signal input is possibly a direct connection to a grid.  I suggest using a ten turn link made of solid hookup wire into a 2" diameter hank, even five turns will work. Connect this link to the hot and shield from the RF generator. Plug the generator into an outlet not common to the radio as well. This more completely isolates the RF generator from the radio so only injection point is the link which can be brought near the grid of the mixer. I do not think that will greatly improve the "booming" audio issue in of itself but may help to redefine the peaks of the IF more correctly.

Any broadly tuning adjustment or adjustment that does not peak has a problem. I have found that RCA IF's wound with litz tend to break strands of wire at the point of attachment. The broken strand(s) will raise the resistance of the coil and reduce the "Q" of the coil...  Some of these RCA IF will repair and peak properly, some will not and require a used replacement...

If this RCA radio uses proprietary mica caps molded with a soft plastic that is embossed with a <> check for leakage. Replace with near exact values, any changes to those tuned circuits will require a re-alignment of the RF/OSC, even pushing around a solid wire...

Good Luck!...  chas