Hi Sven,
I understand your confusion about getting your gourd dry. There is lots of information here on the gourd forum, and each person usually shares their preferred method.
As a rule, gourds of any kind need several months to dry, on or off the vine. You can leave the luffa on the vine and let it dry for the next few months, or remove it and let it dry outside or inside. It still needs several months to finish drying.
My recommendation is to leave the gourds outside where they can have plenty of air circulating below and around them. The frost won't hurt them.
Just be patient and let us know how they are drying. Read through the gourd forum and you'll find lots of great info.

Jan

I try to pick my luffas as they are starting to get shriveled but before they are shriveling, where it has dried as much as its going to without the skin getting brittle - darker/discolored on the outside but still green underneath. Makes it a lot easier to shuck the sking off without having to soak it, I ususllly manage to get the luffa husked before I get into the house, then I spend some time shaking seeds and rinsing it before setting it to dry. I end up with a much brighter sponge that way, as the molds don't get a chance to set up shop inside the drying gourd.

Incidentally, we also found that the top rack of the diswasher is a great way to clean up a new luffa.

Cut them off before it frosts or freezes and dry them inside.