I keep getting email notifications of new posts to my subscribed threads, yet-

… I clicked the box for ‘no notification’ and saved the changes under my profile. Several times.

Whaaaa?

You need to clear out any previously subscribed threads as well. Turning off subscription notification will only affect threads in which you subsequently participate, but any prior subscriptions will not be affected. Go to your User CP, click the List Subcriptions link and delete whatever threads you no longer wish to subscribe to. If you clear them all out, you should no longer receive subscription notifications.