Hi Nicolas,
I had a lot of problem with checkout workflow since 1.5.5 on production site, but everything worked fine on localhost,
what was upgraded time to time when new releases came out.
I went through several times on Faq of payment and shipping setup, and everything was just right.
Finely, I have fund that, saving the plugins in Hikashop not the same like saving in plugin manager, because if was
saved and enabled in Hika, the plugin access field remain blank (should be public) and checkout does not work anymore.
So I would extend the Faq with one more line: Check the saved and enabled plugin access field in plugin manager.
regards, Pal