I would usually have the nut at around my eyebrow height in playing position, the range of movement for both hands works best for me there. Some go lower, especially in roots music styles where you might stay in the lower positions more.
Harmonics are harder to sound than on bass guitar - bright steel strings help, as does playing with your right hand down at the very end of the fingerboard.
Re finding the notes higher up, putting a pencil mark or a sticky dot at the octave can be helpful as a temporary measure. Keeping markers on permanently is a contentious topic, but as a short term thing to help learn your way around it probably does no harm. And on most double basses the heel position helps with orientation around the 7th/8th "fret" region, but EUBs don't all recreate that.
The string heights you're aiming for are probably in a reasonable ballpark. 5mm-8mm is not uncommon for modern jazz styles with steel strings. It's at the low end of the range you might see on double basses in the wild in the UK, but I'd probably do the same on an EUB where unamped projection is not a concern. (I have my double bass down there currently, but with an adjustable bridge I retain the option of going up a little for specific gigs)