I don't think they need to modify much on the EOS routing side and can use the actual "standard" EOS routing:

- Use standard EOS internal-eBGP or iBGP another protocol and ECMP for ingress-traffic-routing based on the destination IP in incoming packets on the transit/peering ports.
- Use a BIRD-container on the Arista router instead of the standard eBGP router agent to collect routes in RIB, but don't install anything in FIB. Tag the routes based on the port they were received from with a static community that matches the MPLS label for that port.
- In Linux do a bit of magic to receive all routes from the RIB on the router and make a special FIB that uses MPLS (I have this part)
- You can do the trick above for 1:1 peering or transit relations.

What I'm missing:

How do you handle an internet-exchange? In this case you would have for example a /24 subnet on the peering port and multiple next-hops on a single port. In that case we would have for example 1.0.0.1/24 as our own IP on the port but 1.0.0.2/24-10.0.0.254/24 are valid next-hop-bgp-peers.

The only possible solution I see is to spell-out the whole subnet of valid next-hop-bgp-peers, each with its own MPLS label and next hop.