In other words, if you buy a suppressor from them, will the dealer in my state charge me a transfer fee? If so, what is the going rate?

Fee is included. It's $70.

It's $64. They charge $206 for the stamp to cover CC fees.

I don't know exactly what they pay the local dealer (maybe $64 minus 3% CC fee? Maybe more?)....but you won't pay them anything per the agreement SS has in place with them.

OP...you can use SSD and use one of their dealers, or you can just pick your own. I have a local dealer that's on their list, but he charges $50 for an NFA transfer, so it would be cheaper to not use their $270 option. (It would also be faster, as the local dealer will file the F4 faster than SS will ) I know some people get charged $100+, and some $0, so it'll depend on your local dealer as to which is less expensive.

$270 SS direct breakdown:
$8.10 CC processing fee.
$200 stamp
$50 to the dealer handling the transfer.
$11.90 to SS for being your paperwork jockey.  

I would say your F4 gets sent faster than through a local dealer as SS sends it off on behalf of the local dealer as soon as the F3 is approved.    

Works out great for the local dealer since all they do is enter it into their log when the receive it, then they process the 4473 when you show up to pick up the item.  They get $50 to store a box the size of a wine bottle for however many months.