Steve, what you are showing as EGC's are actually GEC's, and yes, this configuration puts them in parallel with the Grounded Conductors (neutrals).
This is what I said here.
If a connection is made to the GES in the way of individual conductors from each Panel or Disconnect enclosure, there will also be a parallel neutral path created on these conductors but it is allowed.
Now, even though this is allowed it is not necessary.
What you are not showing in your graphic is the "Bonding Jumpers" (can be the factory supplied green screw through the bar into the enclosure)
With the Neutrals bonded in both enclosures, you would only need a GEC from one of the enclosures or the meter.
The grounding only needs to be done once.