Anyone (even Jack) can move the fabricator. If you can’t then you might have a bug and need to uninstall/re-install.
I’m sorry if that’s the case - I had to do that 4x after an update and with it being a 1.10GB download then that SUCKED.
Still other team mates should be able to move the fabricator.
If you don’t have an engineer you can still get weapons lockers out of: Jack, Fahz, COG Gear.
They will be slow and only hold 1 thing but it is better than nothing.
Some people say you don’ t need an engineer and that’s true in ways but to beat a full 50 waves at high difficulty it will be very hard.
We played a lot in 4 BTW - if you want to do some more I play a little every day just hit me up 
I tend not to have the 3 hours needed for 50 waves of horde but Frenzy is perfect for me and Escape is a good way to level up characters and skills