Does this point to bad RAM?
Yes accessing problem with the onboard memory are the main suspect.
RAM chips, CPU, or the bridge chips (U5,6,7) between the Z80 and Nick bus also are possible.
The Beep test write 00h, FFh, 55h, AAh to the FFh segment, starting the 0. address then continue with the next bytes. You can hear the readed value: low sound are 0 bit, high sound 1 bit.