from your point 1 it looks like you have only completed half the unrecognised NIC instructions... you have to read the article _very_ carefully and understand exactly what it is asking you to do (as it is very easy to make a mistake with that process!)
First, you need to understand what initramfs and vmlinuz are and how they are used for network booting. Vmlinuz is the first piece of code loaded (via TFTP) on PXE boot, and its entire job is to create a RAM disk, TFTP down the initramfs file, decompress it into the RAM disk, then hand control over to that code to continue. Initramfs contains a small Linux micro kernel and basic hardware drivers necessary to start networking, and mount a remote NFS share locally as the system "disk", then hand control over to that full kernel to start running normally.
The full kernel on 0810 (and probably 0710) will likely have the correct network driver for your NIC, however that is no use if the initramfs micro kernel doesn't have the driver, as it will not be able to start networking and mount the NFS share to get to the full kernel... catch 22! It would seem (I am deducing, I don't know for sure) that the NIC "driver" in vmlinuz is so basic that it will pretty much work on any NIC, so that doesn't need to be updated, and obviously the NIC "driver" used by the PXE firmware is able to drive your NIC because it came with the computer!
So the issue is usually initramfs. But you need to understand that there are 2 different initramfs's involved... the first is the "default" one used for _new_ MDs - ie MDs that have never been seen before my LinuxMCE. The instructions for that are at the top of that article. These are the easy ones to follow. The second is for after LinuxMCE has run the initial discovery on _first_ boot of your MD and assigned a device number, rebooted the MD, etc. The instructions for this one is the second part of that article and can be more difficult to follow what is going on because of the chroot bits...
Note that the first one is here /tftp/default/initrd and the second one is here /usr/pluto/diskless/##/boot/initrd... (which is then symlinked into /tftp/## ie different from the "default" location)
It is highly likely that you have successfully modified the default initramfs, so the first part of setting up an MD has gone through, and you will see it as a device in the device tree of web admin. But haven't successfully modified the second initramfs, which is used for all subsequent reboots.
The error message you are getting means that the driver module for your NIC is not loading and so the eth0 interface name doesn't get set up... ie no networking, and without that, you cannot mount the system "disk" over the network, so the kernel panics, as it cannot continue.
Note that the first uses /etc/initramfs-tools-interactor/modules the second /usr/pluto/diskless/<mediadirector-id>/etc/initramfs-tools/modules
You must edit BOTH /usr/pluto/diskless/<mediadirector-id>/etc/modules AND /usr/pluto/diskless/<mediadirector-id>/etc/initramfs-tools/modules before you chroot into the MD's files. And you must depmod before recreating the initramfs, as this is what reads those config files and tells the initramfs to load that module on start up. It can also be relevant if you modprobed the module into the kernel on the core before even creating the MD image.
One thing is certain though, once you make one stuff up, you can go back and try to fix it up but more often than not you end up in knots! It is usually better to go right back to the beginning and completely delete the MD from the device tree (and allow it to delete all the files - that's why deleting an MD is so slow) and starting again, being concious that the new MD will have a new device number, and that often it will detect it as AMD64 rather than i386, and if your core is i386 (which it should be) the chroot won't work... if that is happening it can be a bit tricky to get around, so I won't detail that here unless you confirm that to be an issue.
BIOS boot firmware -> PXE boot firmware -> vmlinuz RAM disk bootstrap software -> initramfs Linux micro kernel boot software -> Linux full kernel