Z Axis inconsistency - Geeetech I3
From the pictures can be seen that you have good lead screws as there is no cyclic anomaly/wobble present at the side. It appears as though the lines at the sides of the print are more or less random X/Y positional inaccurate.

These lines can be caused by various reasons. From what is read you tried to improve the mechanical system by upgrading the hardware. It could still be the case that there is still some backlash or play left in the system (e.g. I had once had too much tolerance on the holes of the linear shafts in the printed X-Z mounts causing similar problems). Vibration should be looked into also, e.g. do you have a binding bearing or a large mass on the printer that interacts with the carriage movement like a spool holder on top of your frame. Or maybe the micro-stepping does not work optimally, so check the stepper driver currents.

If it is no mechanical issue, it could be that you are facing inconsistent extrusion caused by variation in filament thickness or gear slipping or too much tension on the filament by friction in unspooling. Or else a hotend temperature variation. Maybe insulation on the hotend helps.