The shipping FFL should provide the packaging for you. ( I usually do)
Not sure what the guys charging you but you should be able to ship the long guns yourself through the post office without the FFL fee. Assuming the receiving FFL will take it from an individual.
FFLs can ship handguns much cheaper. They can use the post office and avoid the overnight fees for fedex/ups.
As stated above, they'll need to get eyes on the firearm to get pertinent info so don't seal up the box.
FYI. I charge $10 plus shipping for FFL to FFL. shipping for handguns is usually $14 for priority medium flat rate box with a signature.
To give you a pat on the back, that's a very good price for the service provided.
Django. If the ffl is good with it. A FFL can take a firearm from a non resident. They'll just take your info for their records as to where the firearm came from.