I've personally departed IFR many times under the Class D procedures with little to no delays at various times throughout the day. The one or two times I have had slight delays have been no worse than the few times I was delayed under the GAAP procedures. Its probably worth remembering that its not necessarily BK's problem as they often need to await departure instructions for you from Sydney.
As for the transponder bit, i'd suggest the old ANC - Aviate Navigate Communicate... i.e. transponder is probably under the "Communicate" tag... the aeroplane is not going to fall out of the sky if you dont immediately set the 3000 code, so perhaps it'd be easier to establish visual separation (if required) from the other IFR guy, make your calls, then once you're all set up on the way into BK, set the 3000 code.... and if you get too busy with the aviating and navigating, then again, the aircraft isnt going to fall out of the sky because you still have your discreet code set....