E-filing has been broken for around a year now, it's a "Print it out, mail it in with a check for $200" thing right now.
How exactly it's handled will depend on who your friend is buying from. A good dealer will hand you the forms, have you sign 'em and tell you where to send them.
(And one of the best in the business is Silencershop.com, based in Austin Texas. They contract with SOT's in most states and can handle the transfer to a local class 3 FFL -
http://www.silencershop.com/ . My first purchase was through them, but I made the pilgrimage down to Austin to pick mine up.)
As far as if the posting date counts for grandfathering a trust or corporation without a CLEO signature, we're in uncharted waters, we haven't had a "president" make law like this before, so we're not really sure to be honest.
Also, make sure your friend already has the trust or corporation set up. Trust is preferred, even if he already has a corporation, just because trusts don't require anything beyond initial setup whereas a corporation requires annual maintenance.
(Is your friend familiar with the 3 ways of transferring an NFA item? Individual, Trust and Corporation, and the pluses and minuses of each?)