Based on feedback from sites which have unsuitable questions handed to them from other sites (for example: Please stop using Programmers.SE as your toilet bowl):
Would it be possible to require that a migrated question be accepted by the destination site's moderators?
The question Adjust the system to slightly discourage migration over other close reasons suggests a penalty for incorrectly migrated questions, but as was stated in the answers, moderators of one site may not always be able to make a good decision regarding what is suitable on another site (which they may not be involved with).
This could also fulfill the feedback mechanism requested to help educate moderators who migrate an unsuitable question. If the migration is denied, it could contain comments from the destination site as to WHY the question should not be migrated.
EDITED: As I am not a moderator... I may have made the ultimate sin of suggesting more tasks be given to the moderators.
I would like to amend my request to ask that users with the ability to migrate a question be required to accept a question on the destination site. This would hopefully cause the process to be quicker, in addition to less burdensome.