We have ShippingEasy set up so that our Amazon seller-fulfilled orders are re-routed back to Amazon FBA/MCF for fulfillment. In other words, our seller-fulfilled Amazon orders are also handled by Amazon. It's not a conventional set-up but it works for us.
We've set up an Amazon FBA rule to ship our orders automatically. However, ALL of our seller-fulfilled orders fail because all of our seller-fulfilled orders have a phone number WITH extension (ex. +1 347-448-3190 ext. 19869). They have an extension because Amazon does not list the customer's actual phone number. They use a forwarding number to protect their privacy. Long story short, every single order that comes from our Amazon store (seller-fulfilled orders) fails due to this issue.
For reference, we have been using Ecomdash (and we're hoping to switch to ShippingEasy). The way Ecomdash works is they send to Amazon/Dropship only the allowed number of characters (i.e. 20). All other numbers are omitted. A similar set-up for ShippingEasy would resolve this issue. It's working on Ecomdash so I'm sure it's possible to set things up this way.