Creating a new Book collection and choosing «Preview with PediaPress» on https://en.wikipedia.org/wiki/Special:Book sends the data through http:// and their website is browsed without https: until the last step, where it changes to https:// (and sets HSTS, hiding it on further requests).
The $wgCollectionPODPartners parameters look like they should work out-of-the-box with a change from http to https. However, there's an issue with the public pediapress server at tools.pediapress.com in that it doesn't have an appropriate certificate, it is using the general EV certificate, which is only valid for pediapress.com and www.pediapress.com