Site policy is the easiest way around this. IF they have no completed Site Policy agreement, they cannot access the site. At the end of each academic period, quarter, semester, term, year, course section, whatever, run a cron that resets the Policy Agreement field in the User table to 0. This means they have to redo the agreement once per academic period you define.
As it currently stands, the choice activity is complicating things and I suggest is really not helpful. So unless you can incorporate the activity, or something similar, into the agreement, then it will remain an issue for you.