Why is the fluorescence spectrum of pyrene time-dependent? I've got a solution of pyrene and I excite it with a laser. If I measure the emission spectrum 1 ns after absorption, a well‐structured emission with a small Stoke’s shift is observed. 
However, if the emission is measured with a delay of 100 ns, a broad, featureless spectrum with a much larger Stoke’s shift is obtained.  

Is this purely because pyrene has had some time to undergo solvent reorganization and thus the individual excited pyrene molecules have larger differences or is there something else at play?
I think that you have rediscovered the emission of pyrene exciplexes :)

As you have correctly assigned, the structured fluorescence spectrum shortly after the pulse is the emission of pyrene monomers.

Given sufficient time (100 ns), an excited molecule of pyrene diffuses towards a pyrene molecule in its ground state and forms an exciplex. 

Fluorescence emission from these exciplexes is known to be broad and unstructured.