I doubt that makes sense. The feature to force caching assumes that there must be another cache policy preventing caching. You have found a solution by forcing caching, but this solution leads to new problems that can probably no longer be solved because in the end there are only exceptions and the rules for caching can no longer be used in a targeted manner.
I don't know about this course timer function, but to exclude partial areas on a page from caching, there is ESI and ESI should be able to solve the problem with course timer. I therefore recommend you to remove the forced caching. Then the referrer cache rule works in any case. We have to solve any problems with the course timer differently.
So your saying the forced URI setting in LS dashboard does not overwrite the htaccess rule we wrote to not cache referred by websites
Yes, it works and that's why the referrer rule doesn't work either.