Haven't had my 1000A powered up in a couple years, but don't remember any hiss except for a faint hiss in Phono, Tape Head, and Mic, most likely due to the germanium transistors. All other inputs, AM/FM come in AFTER the EQ (phono) board. You could have a noisy tube or tubes (12ax7 or 6AN8's). 6AN8's tended to be noiser for me, I finally found a pair of Matsushita's and they've been good for over 10 years. 12AX7's, I like the GE 12AX7's in it as they are quieter than RCA's and most Sylvania's. But EH12ax7's are pretty good and relatively cheap compared to old stock domestics and Tele's, Mullards, etc.
On the sources that have a RCA Jack, install a shorting plug (AUX, Tape monitor, tape head, and phono 2) and recheck. If they quiet down, start checking the carbon comp resistors (they do get noisy after years. Carbon Film or Metal Film resistors of same value and wattage are smaller physically. And they both reduce noise levels Metal more so over Carbon. You could do one channel worth then compare to other side. (Do the worst side). Also test your 12AX7's, 6AN8's.