Have you seen my Router ID?

There is more than one possible solution for this challenge. Feel free to post your proposed answer in the comments section. We will try to keep comments hidden from public view, so that the fun isn't spoiled for others. Also, don't feel bad if the answer(s) aren't immediately apparent. A number of very bright people have been puzzled by this scenario. Answers will be posted on Friday, September 18th.

Scenario:

R1 and R2 are configured with their FastEthernet interfaces on the same subnet. R1 will be forming an OSPF neighbor adjacency to R2 over the FastEthernet interface, and will also be advertising some loopback networks into OSPF.

R1R2

R1's Relevant Configuration:

interface Loopback1
ip address 1.1.1.1 255.255.255.255

interface Loopback11
ip address 11.11.11.11 255.255.255.255

interface Loopback111
ip address 111.111.111.111 255.255.255.255

interface FastEthernet0/0
ip address 150.10.12.1 255.255.255.0
no shut

R2's Relevant Configuration:

interface FastEthernet0/0
ip address 150.10.12.2 255.255.255.0
no shut

router ospf 1
network 150.10.12.0 0.0.0.255 area 0

Challenge:

Your task is to configure R1 while meeting all of the following criteria for requirements and restrictions:

R2 should see the networks 1.1.1.1/32, 11.11.11.11/32, and 111.111.111.111/32 as OSPF routes in R2's routing table, but they should not appear as IA, E2, or E1.
The output of "show ip ospf neighbor" on R2 should show 11.11.11.11 as the Neighbor ID for the adjacency to R1, even if R1 is reloaded. No other Neighbor IDs should show up on R2.
You are not allowed to use the "router-id" command on R1.
You are not permitted to shut down any interfaces on R1, or remove any of the existing configuration on R1.
No additional configuration may be added to R2, all configuration for this challenge is done on R1.