

I agree that Google has done a lot to stop custom ROMs and many projects have declined as a result. However, they are yet to take more extreme measures such as requiring all boot loaders to be locked etc. (which would damage Google greatly, making this so unlikely as to make the probability of this happening negligible) My bad for not communicating this in the original comment.
The problem with Z axis is most likely either inconsistent extrusion or the printed PLA getting pulled alongside the nozzle. Have you tried lowering the temperature (the printed PLA getting dragged along and oozing are both present), adjusting the Z offset (though unlikely to be the sole problem since your printer should not be stringing this much even if Z offset is slightly wrong), drying the filament (could be responsible for inconsistency of extrusion though unlikely), applying some glue (to improve adhesion if the model is moving slightly when printing), and cleaning the nozzle (some foreign particle is interfering with extrusion) and the sheet (in case bad adhesion)?