Well, if you are not planning on leaving it on all the time, then it can't be the DHCP for your network etc.
I'm kind of where you are.... What I've done is to leave my existing network alone. My test Core (I'm going for dedicated) is just a node on my internal network and is turned off when I'm not playing with it. I have the 2nd NIC and switch and my 1 MD is connected to that. Again, when I'm not playing, both are switched off.
Now, once I have got it all working, put in a production Core and, mopst importantly, got Family (well, wife!) buy-in, I will leave the core on and migrate my existing machines to the "internal" network.
The problem you have is that the whole way MCE "knows" about new devices is from their DHCP request. If it isn't the DHCP server, then it can't detect the devices and you've cripled the system. Add on to that that your MDs are diskless, so rely on DHCP to do a PXE boot from your core and you have a stack of broken bits.
As I said at the start, if you turn off your core, then it can't be your DHCP derver since the rest of your network will be without "leadership". (In your suggestion about putting your router on the "internal" network, you didn't mention wanting to turn your core off
On the cabling front, do you already have Cat5 to your location for your Core? If not, 2 cables isn't much more than 1. If so, you can always get splitters that let you use a single Cat5 / RJ45 for two connections. Alternatively, you could get clever and put in a mini switch and use VLans. There are lots of possibilities.
Finally, noise. That's one of the reasons I'm going for a dedicated core. Put it somewhere where the noise doesn't matter
(Garage, under stairs or wherever).