I have a comment on this question which might be helpful, but definitely not a complete answer.
I would write that comment, but do not have enough reputation yet to do that. Should I write my comment in an answer instead?
Try to flesh it out into a complete answer first, then post it.
Failing that, answer a few other questions to gain the comment everywhere privilege, and then post a comment.
(You've already done the latter, but I'm answering for the benefit of others who might share this question)