Here is an OpenCore EFI folder created using OC 0.7.5 for a similar Haswell system, i.e. Z87 board with i5-4440 CPU.
There are two config.plists in the OC folder, one for using just the IGPU (config-IGPU.plist) the other for using an empty/Headless framebuffer alongside a discrete GPU, like you GTX 760.
The XhciPortLimit quirk has been enabled, as you are using macOS Catalina and don't have a custom USBPorts.kext created for your system. This will work unto Big Sur 11.2. After that you need to have a custom USBPorts.kext for your system's USB ports to work.
You need to read and follow this USB configuration guide once you have booted back in to macOS Catalina -
https://www.tonymacx86.com/threads/the-new-beginners-guide-to-usb-port-configuration.286553/
N.B. The config.plist uses the iMac15,1 SMBIOS, but
you need to add these details to the config.plist for your setup. This will allow you to run macOS Big Sur, if you want to, using the same OC setup. Do not use the iMac14,2 SMBIOS. If you have problems with this aspect let me know and I will see what I can do to help.
To use this EFI do the following:
- Rename the EFI-Share folder to EFI.
- Then copy the EFI folder to the EFI partition on a spare USB pen drive, which has been formatted GUID & HFS+.
- Reboot the system with the USB installed in a USB2 port.
- Press the 'F12' key when Gigabyte splash screen appears to display the Bios boot menu.
- Then boot from the UEFI partition on the USB drive, not the main partition on the USB.
- When you get to the OC GUI boot screen press the spacebar, if the CleanNvram, OpenShell, ResetSystem and ResetNvram tools are not visible.
- Use the CleanNvram and ResetSystem tools in that order. This will clear any issues in the Nvram and reboot the system.
- Boot to the UEFI partition on the USB drive again, and boot your Catalina installation drive using this OC setup.
See if this EFI works.
It is set to display the verbose text, and halt if/when a kernel panic occurs. So you can take a picture of the text if necessary and post a copy here.