Even as someone that plays on 30 or so ping, I have to press space early to hit the zone, add that with the fact that sometimes it takes a second or so for the next stage to appear, throwing you off the balance.
The whole picklocking skill check should be changed where you do fewer checks, but with longer "idle" times in between. So you are still picklocking for the same duration, but less skill checks which are fps/ping dependent.
Also if you do it with lesser checks, you can do multiple types of checks, one is where the bar is slowly moving and then few fast ones so there is still challenge to picklocking (cheap cars don't have as many fast checks, expensive ones have more of them)