I assume the checklist are small things that need to get done and you don't care about tracking them regarding time, etc. But if they are more substantial to-do's, one option would be to create an issue for each item in the checklist.
Is the checklist the same for the tasks? If so, another option would be to create a custom form with a checkbox field and attach it to the task (see attached).
I'm sure there are slicker ideas, but this is what I thought of right off the bat and without knowing more about the checklist.