I just added a proper z-axis to my machine and have also been playing with the settings in lightburn, i can say for sure that z-axis controls are pretty poor in LB certainly needs work but I guess most people using LB are just on 2 axis machines. There is a box in the settings window at the bottom that allows you to make the current settings default for all layers. As far as your z axis moving when offset is zero between files i cannot see how that could happen unless the offset is in your defaults for some layers, maybe noise on the control lines, or if you have 1 layer with an offset and move to the next and have optimize z moves on then its not going to put it back to zero when the offset file is burned. That’s how i keep crashing mine i can’t stand to see the z axis go from z to -35 on every line of the built in focus test but that also means when its done its sitting at -35 and any command after that will use that as zero point unless i tell it to go back to zero with a G0 Z0 command so if i want to do a quick second pass i crash the laser as it tries to move to -65. The z seems to not care what the max travel is set at,it won’t stop at it like x and y.
Along with continuous jog for Z I think the next best feature i would love to see is Home just the Z axis and if i set an origin with z=0 then when i say go to origin it should actually move z not just x and y.