I personally use efulfillmentservice. They do eBay as well.
eBay Fulfillment Center | Order Fulfillment Services for eBay Sellers

 

I have a friend that does this (not in the US) but he processes about the same volume and he is with a super small time family fulfilment biz (usually letters).

He just rang around, this wasn't even a service that they offered beforehand.

My advice, for that volume, ring around locally.

 

I knew a guy that started a business like this but not sure it is still around.... you could check. It started out as Green Sky but later he changed it to something like Sellery or Sellary. It is/was in Dallas, Texas. They would list the items for you and everything if needed.

 

Tonight I just happened to be talking to someone that was saying they use a site called shipstation. She sells on ebay. Check it out and see if it does what you need. She was explaining it but there were others around and I wasn't focusing on what she said.

 

Sounds like a heavy execution idea

Do tell us how it goes.