The only other thing I can think of that might be worth trying is a new Ethernet cable. Have you tried running the cable test in diagnostics to see if the network connection thinks the cable is good or not? If the test shows poor cable quality replacing it might be worth a try even if the old/existing cable worked fine with a previous setup.
I have tested two different cables, both Cat5e and not Cat6, however the same cable worked with the Nvidia 780i motherboard. I did however check the cables using the built-in check in the Intel driver and both cables pass the frequency test and score "green" on the test.
As some earlier posts referred to an F7 Gigabyte firmware to have had an impact I wonder how much does the firmware of the mb actually have an affect to network problems vs the quality of the NIC manufacturer's drivers?
Just trying to understand if the issue here is the capability of Gigabyte to keep the NIC stable, or if the NIC drivers are fundamental to the stability/performance, and, sorry to say, I should be looking for another chipset in my next NIC as hinted above?
In an unexpected turn of events Gigabyte support Contacted me suggesting me to upgrade to beta BIOS F12p. I then removed the Realtek NIC, upgraded the BIOS, reconfigured my old BIOS customization (like enabling VT for my virtual environment) etc and restarted. Lo and behold, now I have my full gigabit speed back. So my apologies to Intel for questioning the driver or device capabilities, the issue was actually motherboard BIOS deficiencies corrected in the latest beta BIOS for the GA-X79-UD3 mb.