SOLUTION (for me at least).
Use AppleIntelE1000e.kext, v3.3.3. Later versions cause this problem. I tried v3.3.5 and 3.3.6, but not 3.3.4 as I did not have it lying around, and both cause the problem. I tried installing them in S/L/E and L/E, one at a time.
My MoBo (GA-Z77X-UD5H, rev 1.0) has an...