OP asked: "May I lawfully ship a firearm directly to an out-of-State licensee, or must I have a licensee in my State ship it to him? May the licensee return the firearm to me, even if the shipment is across State lines?"
Which seems to imply they are shipping the firearm for repair or gunsmithing. This is one of the very few exceptions to federal laws on the interstate transfer of a firearm.
The rules for shipping a firearm for gunsmithing/repair are clear. However, it's a big assumption that that's the situation here without a clear statement to that effect.
What if the OP shipped a gun to the FFL of an out of state buyer, who decided he didn't want it and wants to return it?