Hello Espen.

All the major alpine clubs (DAV - Germany, OeAV - Austria, CAI - Italy, AVS - South Tyrol, SAC/FAT/AAC - Switzerland, CAF - France, LAV - Liechtenstein, PZS - Slovenia, ...) and even some alpine clubs of countries outside the Alps (Belgium, Netherlands, Luxembourg, ...) tread members of one association on their alpine huts like own members (so-called "Gegenrecht").

In Austria there are even additional agreements ("Gegenrecht - Österreich") between further Austrian clubs (e.g. ÖTK with his hut at the M-V route: Tuxer-Joch-Haus) and the OeAV and the DAV: Members of one of those clubs are treaded equal to own members - members of alpine clubs of other countries are EXCLUDED there.

Therefore from my point of view becoming member of a section of German or Austrian alpine club makes the most sense for you.

You can read a current overview (in German) at:
https://www.alpenverein.at/kufstein_wAssets/docs/Gegenrecht2014.pdf

Which section you choose doesn't matter, but they have different prices for membership (because the offer different additional activities and hardware for rent - but of course that's completely irrelevant for you) and sometimes they demand additional fees for sending the membership card to foreign countries !

K2.

P.S.: Today I'll meet some members of my home section and I could ask them, how much a membership would cost for you.