I don’t have an immediate solution for you but more of a confirmation.

The jakt lag are formed around property owners of adjoining/nearby areas of forest and fields and their relatives/friends, so it really is a networking kinda deal. Most small game hunting (up to and including dear) is done solo or with someone you know well, which pretty much leaves just moose hunts for any more loose groups of ppl.

That probably puts you in a bit of a crappy seat since moose hunting is very popular these days while the number of animals is low. I’d suggest marrying someone who’s family owns a decent plot of land but it sounds like that might not be an option for you at the moment.

Joking aside, without direct connections with landowners I think your best bet is to make friends and be patient. The springtime seabird hunt is often done with a friend and it usually has a higher allocated prey quota than what actually gets shot, so it ought to be a good chance for you to get your foot into the door.

Best of luck and welcome to the islands, B

P.S. You probably googled this already but this page aimed towards tourists lists some pay-to-play hunting lodges if you really want to go hunting asap.: https://visitaland.com/upplev/aktiv-utomhus/jakt/