Is it possible to exclude certain demographics from LinkedIn Ads?

Linkedin has a policy of non-discrimination, which is fair, but we are having the following issue:
- our ads are delivered for people who permanently live or work in the US.
- I won't get into details of our field, but we do make a lot of business with legal, highly qualified immigrants
- One nationality in specific makes up the majority of our leads, but for a few reasons, they are not in a rush to buy our product, which increases our cost per lead and, obviously, our conversion rate, not to mention a good chunk of our time wasted
- LinkedIn does not give an option to exclude based on demographics nor language, which I understand, but at the same time, it creates tremendous cost and inefficiency

Has anyone ever faced a similar situation?