Why? "Let's say" : The electronics in the GFCI have died and no longer work.
When Manny says "let say", I hear a hypothetical inquiry, and when he says "the gfci going to the laundry room is replaced" I interpret the most likely possible meaning that he is asking about, is a GFCI receptacle mounted at the Laundry Receptacle Outlet, especially because he goes on to say there are no full size spaces in the circuit breaker panel. (GFCI breakers are full size).
If the local authority will not accept applying 2014 NEC 210.12(B) Exception to 406.4(D)(4), and only allows replacement of a device as in 210.12(B), then all that needs to happen is to install the OBC AFCI at the first outlet of the existing branch circuit, which, in the case of this laundry room, should be the very outlet we are talking about. There is no requirement in 210.12(B) to also replace the existing homerun wiring for a receptacle device replacement. Because 210.8 requires any laundry receptacle to be GFCI protected, the OBC AFCI can't have receptacles, and must be upstream from the new replacement GFCI receptacle, which is why I recommend finding the available blank face OBC AFCI and installing it side by side the GFCI receptacle.
As Wayne Whitney points out, there is debate whether an blank face OBC AFCI might be considered an Outlet. Even if the AHJ considers it an Outlet, it, the blank face OBC AFCI, is NOT a receptacle, so there is no complication from 210.8, and the assembly, in my opinion, works, satisfying the 2014 NEC.