The Key in my opinion is in this sentence:
The register data in the response message are packed as two bytes per register (word), with the binary contents right justified within each byte. For each register, the first byte contains the high order bits (MSB) and the second contains the low order bits (LSB).
Try to read a simple register like 771 e772 are one word length
I’m getting closer, seems like the HA Module offsets the register by 2.
It’s reading adress 55 when it’s suppose to read 53, if i offset it by 2 it reads something completly different. That’s the meter “total consumption”.
With the “current power” it worked by offsetting by 2.
Figured it out now, apperently count 1 offsets the register by 1. Count 2 don’t, it offsets differently somehow.
Thanks for your help! With this many variables 4 eyes are better than 2 
Happy to hear that, coul you post your configuration?
Modbus example are not so much in the forum and your config could be help someone else