Three Branch Office Connectivity

I currently have three branch offices connected in a triangle with the following scenario:

Each of the three are connected via serial to point-to-point single T-1's.  Each link currently has it's own network.  Two serial cards in each router.  One going to each directly connected site.  Pretty standard I guess.  Three inside networks (10.1.1.0, 10.1.2.0 and 10.1.3.0).

Router A---------10.1.12.0----------Router B
Router A---------10.1.23.0----------Router C

Router B---------10.1.12.0----------Router A
Router B---------10.1.13.0----------Router C

Router C---------10.1.23.0---------Router A
Router C---------10.1.13.0---------Router B

I am going to be getting rid of the T-1's and converting to a 10 Mbps fiber based MPLS (AT&T calls this OPT-E-MAN) which is actually a switched network and not a routed network although I can route it of course.

I am not going to be getting rid of the routers I currently have (Cisco 2811, 2821 and 2851) because they are already doing other things and I would like to keep a segmented routed network.  Router A has two PRI's for voice and an FXO card for paging, Routers B and C each have 1 PRI for voice and one FXO for paging.

Each router has 1 extra available ethernet port.  I could configure the ports on Routers A and B to be on the same network (say 10.1.4.1 and 10.1.4.2) and they should talk fine.  But without another ethernet port, what is the best way to connect Router C so it can talk to Router A and B?

Can I put three routers with IPs on the same network, say 10.1.4.0, plugged into the same switched network and be able to get to the correct network on the other side of the router?  I am thinking this should work.

Proposed:

Router A------ 10.1.4.1----------- (with the 10.1.1.0 network behind it)
Router B-------10.1.4.2-----------(with the 10.1.2.0 network behind it)
Router C-------10.1.4.3-----------(with the 10.1.3.0 network behind it)

Will this route OK?

Or is it possible to subinterface an ethernet port so that one port would reside on two networks?

Maybe I am overthinking this, but any thoughts would be greatly appreciated!