Current measurment at a high potential
I came up with a now working solution which is precise.

I used a shunt in the circuit and an Arduino with an 16-bit ADC (MC3426). The Arduino connects via a cheap wireless module to another Arduino which is connected to my display. 
By precisely measuring the shunt and testing the ADC the result is good enough for my purpose.
The galvanic separation comes from the wireless connection between the two arduinos.

If someone wants more details, write me.