No matter what order you install the carts, you always get the error on the last insertion, regardless of which slot is last? In other words, it's not confined to a specific slot?
If so, that sounds like it's not a hardware error. Maybe a firmware re-flash will cure it.
If not, replacing the cart receiver is expensive. If it's like my 9800, you'll need to purchase all the slots on one side. It's a single unit.
(edit) Oops, missed the part about third party carts. Agree on testing with genuine Epson carts before proceeding.