John,
I just noticed, in your jperf results it looks like you forgot to set TCP Window @ 64k.
I was sorta joking about throwing money at more nics. I don't think you should need to do that. I have the same 8111C in three computers, including my unRAID server. Unfortunately, unRAID doesn't ship with iperf and I don't know how to add it. But jperf between my gaming PC and HTPC looks like this:
A bit under 800MB/s. The only thing I tweaked was TCP Window Size - to 64k from whatever XP defaults to (I think 8k). I'm losing a little speed right now because I'm transcoding video over my network
On one side is a Gigabyte GA-G31M-ES2L. Realtek 8111C with driver version: 5.720.327.2009 (3/27/2009). XP Pro x86.
The other is a Gigabyte GA-MA74GM-S2, 8111C, driver version 5.708.1030.2008 (10/30/2008). XP Pro x86.
I wired my house with cat6, through a patch panel, through a TRENDNet TEG-S80g unmanaged gigabit switch.
Re-try your jperf test with TCP WIndow set to 64k. I bet you get better results.
Try jperf/iperf between some other machines. Any machine with a gigabit NIC on the PCI express bus should do 800+ MB/s, assuming everying's working properly. All of your machines except for John appear to have their NICs attached to the PCIe bus or directly to their chipsets. This should all be good enough. Try between any of them except for John.