Using $recipients in a system filter gives me another problem: how can I do a string lookup if $recipients is a list of addresses?

Check out the section of the filter specification called Testing a list of addresses. If that doesn't help, you may have to resort to calling an embedded Perl interpreter - but that is expensive.

In Exim 4.67 you will have a number of list processing expansion items (map, filter, reduce, forany (condition), forall (condition), and addresses to convert $recipients to a list usable with the previous) at your disposal.