And are the blue and grey lines also physical links? This would mean CE router #3 from the left would have … 6 uplinks? If just counting red that would be 4?
Default route is not preferred because only 1 of 8 of their public IP networks not reachable through primary in that case BGP automatically switchover only to that route to lower MED or else.
Oh so is this concern more about their intersite connectivity than their connectivity to the internet? If their AS path for their “internal” routes is going to be 65106,65000,65105 on your diagram (this would be Moultrie to Tifton North I think), then the best path would be Tifton 2nd St because it doesn’t have to traverse the path to Vienna. (Also I’m making up that your ISP AS here is 65000; I don’t think you specified.)
This is going to involve a lot of manual policy work on your part because BGP is going to inherently hide all of the topology details of your network. What you could do is to set up a series of BGP communities that correspond to the ingress router, so say 65000:1 is routes learned from peers on Tifton 2nd St, 65000:2 is learned from peers on Tifton 4th St, etc. You can then build a routing policy for each of your routers that will announce the lowest MED for routes that originated on that router and then a higher MED for any other routes.
The customer would then receive from each upstream peer: 1) a default route (for internet traffic) and 2) all of their own routes from other sites with two possible MEDs. In the token example, as long as Moultrie still has a link up to Tifton 2nd St, they will see and use the lowest MED down that path to Tifton North. If that whole path fails then they will still have a route to it via any of their other uplinks.