The replica was from a touring prop show that was exhibited in science museums in the mid-late 2000s. I saw it sometime around 2009-2010 (the museum was showing Star Trek '09 in IMAX, so that puts a lower limit on the time frame for my visit). Aside from a bunch of props and replicas on display they also had a partial TOS bridge set and other stuff (including, apparently, a GoF that I don't recall at all).