Solution
Should someone else come across this, the answer is "nested resources". In my case, I solved it by doing this:
Route::resource('clients.contacts', 'ContactsController', array('except' => array('create', 'index', 'show')));
A simple php artisan routes-call reveals that the routes created for the ContactsController should contain two parameters in the url, one client id and one contact id (where applicable). Handling contacts is now a cinch in the controller and can be done in the proper RESTful way.
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