@profcrane
Sounds like you could benefit by leveraging the To Do list, rather than disabling it. A lot of people struggle with this and I've experimented with different things and finally came up with what I feel is the best solution.
Make your due date for the discussion the day the initial post should be done. This will disappear from the To Do list as soon as the students make their initial post. By making the due date the day the discussion ends, then students don't get the first date (unless they pay attention to other things you say/write) and once they complete their initial discussion, the item is gone from the To Do list and there's nothing else to remind them to go back in.
After changing the due date to the date the initial post is due, then go into the Assignments page and create an assignment for the second due date. For the description, make a note that they need to do the follow-up responses to the discussion and provide a link to the discussion. Change the "Display grade as" to "Not Graded". This will keep it from appearing in the gradebook or having a grade, but it does place it on the calendar and on the To Do list. The only way for the student to get rid of it is to X it out as having been completed. The item will show up in the To Do list with the prefix of "Complete" so I change the title to match that. "Complete Discussion 2 Response" would be called "Discussion 2 Response" as the assignment title.
I would also set the Available Until date to be the last date you want students to post, the one used in the non-graded assignment. This way, students cannot post past the time when the discussion closes.
Switching things around does not work. Putting the due date as the end date removes it from the To Do list as soon as people post, so having a non-graded reminder of the initial due date doesn't disappear when they post, so they're like "What happened? I posted that?" and the second reminder (the due date one) disappears at the same time.
I tried adding events to the calendar rather than non-graded assignments. Those show up on the calendar but not in the To Do list. My students who used the calendar were fine, but those relying on the To Do list didn't get the message and struggled. Make it a non-graded assignment so the To Do list users get the message.
On a non-related issue, I set the students to not be able to see other posts before they do their own and then disable the ability for them to edit their posts. That keeps people from putting in gibberish to see what others have done, then editing it to look like it was their original first post.
That is the best technical solution I've found. Getting students to be more responsible or work ahead of time is something that it doesn't fix. Trying to trick the students or setting due dates before the real due date doesn't work well -- mine just figured out how to figure out when it was really due and then waited until then to attempt it. Instead of making them fight Canvas, help Canvas work for them.
You can do the same thing with your other issue, but then it would show up to everyone, including those who have already done the exam. If the exam is in Canvas, then a better way would be to go into the Gradebook for that assignment and choose "message students who" and send those who haven't completed it a reminder. That way it keeps it out of those way of those good students who did it on time. You could use a differentiated assignment (too much work) to assign to just those who didn't turn it in. Or in the instructions for the second assignment, just make a note that they should ignore this reminder if they have already completed the exam.