Flesh out the modal description for migration, specifically as to what makes a question 'complete.' Right now, the description reads:
This question is out of scope on this site but is on topic on another site in the Stack Exchange network and should be moved there. This close reason should only be used for questions that are of good quality and complete.
I think that adding more context about that 'complete' part would be helpful. Since your commentary says that the intent of this message is to clarify that we shouldn't be migrating crappy questions, perhaps something along the lines of the following would have a similar effect, without having room for confusion regarding what actually makes a question 'complete':
This close reason should be used for questions that are of good quality and meet the standards of the site to which they are being migrated.
I also think that it would be helpful to link to the other site's 'on-topic' section in its help center. ([site].stackexchange.com/help/on-topic) This would allow close-voters to make sure that they aren't migrating a question that is in fact off topic on the other site as well.
Edit: this would have been useful when this question was migrated from Christianity.SE to English.SE. Sure, it seems to be more about English than about Christianity, but it still doesn't meet our site's 'please include the research you've done...' close reason. (The migration was eventually rejected and it's now back on Christianity, where it's also been closed.) This probably wouldn't have happened if the user(s) who migrated it to English had been able to easily access our help center.