Upgrade mac pro 4.1 to 5.1 does not work (it just reboot normally)
First, check the requirements:


64bit EFI needed (MacPro 4,1 has it)
latest firmware Update (You seem to have this)
Do you have enough memory and CPU? (I upgraded my MacPro to 32GB RAM and 2x QuadCore 3.2GHz CPU.)
Metal capable GPU like newer nvidia 960/980/1080 GTX?


I am running Sierra 10.12.6 fine on my MacPro 3,1 with latest 1.5 firmware, but I used the installer coming from http://dosdude1.com/software.html, which creates a bootable USB media to install from. That worked like a charm.

So I suggest you try the software from dosdude1 - there is a perfect instruction page how to build the installer from the original Apple Installer and how to use it. (Never ever forget to apply the patches regarding software update provided by the dosdude1 installer!)

I already tried to upgrade to High Sierra and got the feedback from Collin aka dosdude1 that I would need a metal capable GPU, because I got several weird hang ups with my ATI R9 280X during the installation process. Therefore I need to buy a new Nvidia GPU, preferably a 980GTX.