A brain-busting routing question

Let's say I have three routers, and each router has its own route to the Internet.

R1 --- Internet | R2 --- Internet | R3 --- Internet 

I can set up OSPF so each router knows the best path to any destination on this routed network. However, I need a way for some traffic on R1 to reach the Internet when using R3 as the gateway. Normal L3 routing makes it easy to use R2 as a gateway, so don't think about that. However, without a L2 network to help, there's no way for R2 to tell between traffic destined toward it and then the Internet, and traffic going to R3 and then to the Internet. Is there a way to do this? I thought of a couple methods: 1. L2TP VPN. This would technically work, but is a nightmare to set up because it has to be done for every single multi-router link, and in my network, that's a lot of links. 2. MPLS. This could actually work better, but some kind of setup still has to be done on every link and I don't know how to do it. I need a simple setup where R2 would look at the MPLS packet and immediately know that this packet isn't intended for it, so it uses regular IP routing to send the packet to the destination, and only use MPLS to see if it should take that packet and send it to the Internet using its own gateway.

I would want to do this in order to set up a kind of load balancing for R1, so if I had a mesh network, I could take advantage of multiple routes to the Internet and have it dynamically recover from link losses with OSPF.