@Carsten *****
I think you are confusing what they ask for and what you can provide, you just upload the data page of your passport again for proof of residence and proof you can use that consulate, It's the eVisa system, there is no issue with doing that at all.
BUT
now we're just going round and round on the minutia, so you either apply when you're back in Germany via the eVisa system or you come back and go to Lao to get the Non-O visa
I wouldn't go get the Non-O first then exit the country, (meaning you need a re-entry permit) then come back and get the year.
Just get your trip to the west out of the way come back in visa exempt, then go to Lao and get the Non-O single entry.