Though we are BB users, my understanding is that all LTIs work more or less the same, so this suggestion could work for all using it, not just BB; hence putting it here, not in the BB area. 

When setting up an assignment, it automatically creates a due date precisely (down to the last minute!) 4 weeks from the set up point. It sets the post date to be the same (which, for something that's manually graded seems a little odd ...)

I think that it'd work better if the user can set both up manually. The absolute ideal to me would be to have a default time between the due & post date - so that the latter only needs to be adjusted sometimes. If the institution has particular requirements, they could have some prefilling. 
e.g. A particular university decrees that all assignments are due at noon. Then have the time in the due date set to noon. 
b: A different university allows disciplines etc., to set the due time, but require all feedback to be 4 weeks later. Then, once the due date is set, the post date automatically fills itself with that. 

Allowing admins to set those kind of defaults would allow for everyone to have the settings that work for them & staff only have to adjust timings (once the due date is added) if they have a particular scenario that differs from the norm. 

Thanks.