Perhaps the faster communication speeds in BOT were due to a network of subspace booster relays, relays which had been mysteriously destroyed prior to the events of TEI. Yep, the very events which led to the clandestine investigation by Kirk in the first place.
It could be that the "3 week" figure is the speed of natual subspace communications, without the benefit of boosters. Otherwise, we are talking about the events in TEI taking place 168 times further away than the ones in BOT. That is a LOT of light years!
They don't have to be destroyed - Enterprise simply has to be deeper in space in TEI where there are no subspace relays.
That's very possible as well. The only thing we know is how long communications will take but there are variables that we don't know:
2. Subspace conditions between the location and Starfleet command