For $20-25 for a controller board and $25 for the WizNet board and $5-15 for sensor/relay/controller and other bits, that is $50-75 per node.
I had in mind the all-in-one module/chips like the W7100 and W7200. I don't know of any low-cost boards, though.
The [SLIP/PPP] router side should be easy enough
Don't forget about the added cost. Serial-equipped routers tend to be more expensive per port than ethernet 
but I'm unsure about the node IP stack. Any sort of non-IP physical layer introduces translation layers...
IP is a network layer, not a physical layer. SLIP or PPP is a link-level protocol that runs underneath IP, so you'd still have all of the IP (and up) layers; SLIP/PPP essentially replaces the ethernet drivers.
more along the lines of a really basic SNMPv1 implementation.
I have never seen a "small" snmp. The 32k has to support your app, PLUS all the tcp/ip/link/physical drivers. The 76-line "UDPSendReceiveString" example for Arduino is about 10k bytes of code, even though it's using a chip that does the IP/UDP for you. If you use a lower-level chip that needs to implement arp/dhcp/ip/udp/etc, 32k is pretty much gone before you start.
I just built tinysnmp tinysnmp/INSTALL at master · segfault87/tinysnmp · GitHub using clang -0s
on an x86-64 box and it ended up being 53325 bytes.
Statically linked with all the necessary default libraries?
I think the most promising thing I've seen was the Stellaris Ethernet/Serial "eval module" ( http://www.ti.com/tool/rdk-s2e )
Reasonably powerful and tiny CM3 CPU with built-in ethernet (incuding PHY) But TI deprecated the whole Stellaris product line, and has not yet introduced a replacement ethernet-capable part 
There are a bunch of processor chips with built-in radio transceivers of various sorts, which is sort-of interesting, but they tend not to implement IP stacks (BT, BTLE, Zigbee, ANT, etc, etc, etc. All of which have in common that they don't directly gateway to IP infrastructure
) Note that these are typically chips with 128k to 256k of flash, and IT'S ALL USED UP by the network stacks that are frequently packaged with them. And/or they don't let them be used programmed. The TI CC3000 module is attractive, and does WIFI/IP/TCP (!), but ... Radio is also a nightmare from a regulation point of view 