to further clarify It seems that it should be close of next business day but with proper records can be 7 days
"1. Dealer Acquisitions:
Generally, for licensed dealers the purchase or other acquisition of a firearm shall be recorded not later than the close of the next business day following the date of the acquisition or purchase. However, if commercial records containing the required information are available for inspection and are separate from other commercial documents, dealers have 7 days from the time of receipt to record the receipt in the acquisition and disposition (A&D) record."
atf.gov/firearms/qa/how-much-time-does-licensee-have-record-acquisition-and-disposition-firearms

Brian, I would show up at the store/range ASAP

AT this time I would print out all the paperwork I have and be at the range demanding to speak with the manager I would also advise Buds of the situation. Soon after that I would be calling a lawyer and contacting BATF as I am sure there are rules covering when guns must be checked in (if I remember right from when I worked at a range it was immediately upon receipt of the firearm )

Probably now Brian. here in NC I have gone in and received my firearms on the same day as reception by my FFL. It does not take two weeks to "sign in" firearms. I would honestly check other local FFL's and ask their firearm check in time. If nowhere near 2 weeks, I would drive a little further for better service.

I would go in person, some shops wait until their gunsmith has had a chance to go over the firearm. That is a surprisingly long time tho, I would also contact Buds after you go to the FFL in person and they aren't able to transfer the guns to you. Unless they show you a policy that states they cannot release them, you should bring proof of your purchase and get them as soon as you can physically go there.