I think gnu screen has the right idea here: ctrl-a.
And you say z is close to control - does that mean you use emacs without shift lock as control?! (I mean sure, still closer than b...).
When I used Mac in 2009 to 2012 it depended on the application you were using:
Some used fn+left/fn+right, some used CMD+left/CMD+right and I think ctrl and/or alt + arrow keys were an option too.
ctrl a/ctrl e would work everywhere I think but I didn't use those as they didn't work with shift to select to the start or end of the line.
As a keyboard type of person this was a major part of what drove me away from Mac despite its many advantages :-(
I know, because I have triple-shift-press mapped to shift lock on my Ergodox. It's... usually better, but sometimes I type a @#$%@#$% swear word when I mean to enter a number.
C-a (like in screen) would be even better but as others have pointed out it masks going to the beginning of line which is very common.
C-z is very rarely needed. C-q/C-s would be good candidates also as I don't think I've ever needed flow control in this century nor the last one, for that matter.
Presuming Shift Lock means Caps Lock, that and Control are both close to Z on my (Apple) keyboard.