You actually CAN instal Mojave on a 4,1 flashed to 5,1 with the 144 bootrom from a USB installer with a GTX780..if it is fflashed or not i do not know, do not know how to check..but I do get the boot screen .
I thought too you could not install to a clean system from a USB installer of Mojave...but I did eventually find a download of Mojave that does install from clean where an Upgrade woudl not work.
You could run the installer from High Sierra and the machine would reboot..then the Mojave installer would say ..No Cant do it." No metal support..despite the fact that when the system is running you do see Metal 1,3 ' in the system info.
I am afraid that I cant tell you WHICH or how I downloaded the correct version of Mojave installer to write to a USB stick..but I can tell you it does work ..I am keeping this USB installer save on it s32GB stick now for future. It took me maybe 1 week of mucking about to do the clean install without going through Lion.High Sirerra and finally Mojave.
I had multiple different installers for Mojave, downloaded from MrMacintosh and app store or stored on variosu HDD's i have around with software on.
But if you want to install Mojave from clean install and have it re-create the Recovery partition with the GTX780, then yes it is actually possible..but do not ask me how...just keep trying
Edit
I looked through my browser history...it is possible it is a patched Mojave install from dosdudes.
cant be sure either way..but if it helsp someone get a clean install of Mojave then all is good.