[35Z5]

Scott, how many ohms per volt is that meter?? If it's like 20K ohms per volt, it's no doubt loading down the reading. If you were using one of those cheap Harbor Freight Chinese(you love so much) meters that was a megohm per volt, voltage would be higher. The 270K is fine, later radios used 330K or even as high as 470K for plate supply. Current is so miniscule a ¼ watt would be fine.

For noise, disconnect pins 4 & 5 on 6SQ7 to see if it stops(radio should be silent). If it does problem is ahead of audio amp in the RF/IF circuitry, may have a flakey IF transformer or cap inside. These aren't the transformers that are famed for noise problems, but I had a GE that acted exactly same and was the IF transformer.

Actually you can more or less tell with the heater test setup of 6SQ7 pictured. If you have additional leads, connecting pins other than 4 & 5 would be a valid test.