Thanks! Maybe their PMOS nature (P-ness?) is the reason for the annoying voltages? I mean a (contemporary) four-phase-logic shift register wouldn't need those voltages, and of course neither do CMOS shift registers. Though I guess a 1024-bit CMOS shift register would still need a pretty good clock drive current, especially if fabbed at those sizes.
The Apple-1 display used the Signetics 2504 shift register: https://www.applefritter.com/files/signetics2504.pdf
It also used a Signetics 2519 6x40 shift register to hold one line: https://www.applefritter.com/files/signetics2519.pdf