Ok, I've tested this pretty extensively now. Here are the symtoms I am getting:
My NICs, eth0 and eth1, do not exist at all (ifconfig -a does not show them), even when the appropriate modules are compiled straight into the kernel (ie, not modules).
And I can reproduce these symptoms by booting any kernel compiled on LFS (any kernel that isn't the one I initially compiled in the LFS book, on my debian system).
Can anybody tell me what I'm doing wrong? (I also posted this to lfs-support, though that email was probably a little less clear).