I've tried similar to the first when using fresh yeast not dry (the packaging of the dry says this preliminary dough was not necessary) with only little difference, though that was still with melted butter, not merely softened.

I am kneading before the first rise, so I'm not just mixing the ingredients together, but possibly not kneading long enough. Neither of the three recipes for Hefezopf I've consulted asked for two rises before the braiding, but I could try that. Over in the comments on DW someone suggested a "window pane test" to see whether the dough was kneaded and stretchy enough.