Ask HN: Publishing a copyleft book

I plan to spend much of the coming academic year writing a book "out in the open": sources under version control, hosted in a public repo, under a copyleft license. But I am also an untenured researcher, and need to build up my publication record, so I'd like to secure a contract with a conventional academic publisher for the hardcopy format. In the humanities, writing and publishing books this way is not at all common, so I would appreciate any pointers to the usual or most effective roadmap:

Should I approach a publishing house first with the idea? Does making the book copyleft put off publishing houses? Other gotchas I should bear in mind?