In the Administration section you can say that "Non-Members" have the permission to view issues in projects they are not member of.

But this works only for public projects. In our case we can't make all projects completely "public" as it would expose them too much. But adding each user as "reporter" to each project would cause a lot of noise on each user's projects page. They would see a ton of projects while they are probably only directly concerned with one or two.

Now if an issue they created is moved to a project where they don't have explicit access, they effectively lose all access to that issue.

I think it would always make sense to let a user see his/her own issues. No matter where they are located. Optionally, this could be made a setting in the permissions page?