Hi, Davin. I guess I'm a little confused as to why the three main controls you have mentioned for the assignment module (lock changes, prevent changes, and use cutoff date) are not satisfying your requirements.
As someone who has used the assignment module extensively for writing workshops where rough drafts can sometimes be VERY rough, I will say I absolutely needed the ability to allow my students to submit a new draft to me between the deadline and the cutoff date if they completely missed the mark on their original submission (and by "missed the mark," I don't mean they fell short of a good grade; they actually missed the point of the whole exercise the first time they tried it or some other similar misunderstanding occurred). It is part of the learning process for developing writing skills, so with that type of assignment, deadlines really are just metaphors.
You are right, though, at a certain point, they should not be able to change their work and should have to live with their submission as is for that particular learning experience. The cutoff date worked for me there.
Where I needed even more restrictions, I would also employ "restricted access" dates or other criteria so that they could not change work after whatever date I communicated as the absolute last day they could pull that assignment back into a portfolio somewhere (for me this was usually the end of the term).
Perhaps restricted access would give you the additional "off" switch you are looking for on editing requirements if the other options are not working for you.
If you don't find this option available to you in assignment settings, you just need to turn it on at the site level in Site Administration>>Advanced Features. It is a small tick box for conditional access.