The chipset 8111C uses the r8168 driver not r8169, which is your problem. It is incorrectly loading the r8169 driver to run an r8168 ethernet port, thus it fails and says link down.
That is what the patch is all about in that article. You have to remove r8168 as a valid code for the r8169 driver (because r8169 cannot drive r8168) and recompile. This effectively stops the kernel from loading that drivers as it no longer thinks that the driver is valid for that ethernet port (which it isn't! bug!). Then install the actual r8168 driver, and depmod it. That will then allow the kernel to see the r8168 driver as valid for the r8168 port.
Don't forget, when you are doing this, you are mod'ing, depmoding, compiling and installing the drivers on your core. You then have to do the equivalent steps to copy these changes into the diskless image for your MD otherwise it won't make any difference. It can be complex, and easy to get confused as to what you are doing, but following the articles very carfully will get you there. Bottom line is, just having the drivers in the diskless image isn't enough, afterall the machine has to at least boot far enough on LAN before it can even access the diskless image (a catch 22!).
This is what the initramfs and vmlinuz images are about. They get loaded via tftp during the PXE boot using the BIOS's NIC driver. vmlinuz coordinates to create a ramfs and expands initramfs into it, then boots from it. This is like a linux microkernel that is used for mounting the boot share over the network and downloading all the files needed to boot the real kernel. Thus the updated drivers and configuration not only have to be in the diskless image (ready for the "real" kernel to use), but also have to be embedded in the initramfs image so that the "microkernel" used for booting can still drive the NIC once it takes over from the BIOS's NIC drivers. If it doesn't, or isn't configured correctly, the kernel will panic at exactly the spot you indicate ... simply because it has lost control of the NIC and therefore the boot process can't continue... deadend.
What this means is, your PXE appears to be configured correctly, as does your core and network - the MD is successfully loading the images and booting the initramfs image, but either the patch isn't done and both drivers embedded in the image, or the depmod isn't done subsequently to "activate" those changes. The initramfs commands in the article are taking drivers and config from the diskless image and recreating a new initramfs image for you...
Thus, patch the drivers, recompile and depmod them on the core.
Then use the rebuild image button to create the diskless image, which will draw upon the files on the core (including the ones you have modified)
Confirm that the diskless image now has the modified drivers
Then use the article to create a new initramfs image from the diskless image's files
Then you should be able to boot and get past that point.
(PS, Tip: make sure you understand what is happening when you do the CHROOT bit, and keep clearly in mind when you are performing tasks on the core vs when you are actually performing tasks on the MD via the core (because you can't actually do them on the MD yet cos its not running!))