The Intel Pro/1000 is supported ( I am speaking from practical experience, not by looking at the Hardware Reference manual ). But as
jamesutz hints at ... there seems to be a variety of "controller" implementations. I am no expert on this, but I thought I would report that I have several Supermicro boards that work perfectly fine, and looking at their manuals they all use the "Intel Pro/1000" designation, and upon further inspection list two different "controllers": Intel 82541 and 82547GI.
So ... check out what controller is being used (the same board manufacturer may use different versions even on the same product over a period of production) and report back which ones you have/have-not had success with.
jamesutz should confirm that his controller (hardware ) works under another O/S first (Knoppix, Windows, etc). If yes, then the 82573E won't work in NASLite, and unfortunately the drivers can not be "patched" or "merged" by the user. Only Serverelements can do that.
Hope this helps.

Georg