After a lot of fiddling with the supports and a few repositioned parts, prints started to come out great...
Now printing the final (and easiest) part, the base.
Anet A8, sliced with Cura 3.1
PLA, 0.1 layer height, 40mm/s, 15% infill, 195ºC / 55ºC
Support settings changed from part to part