Bringing a complete power unit map from the dyno in Sakura into the ECU of the car shouldn't take make than 4 minutes, maybe even less if Internet is good
Flashing these Things is fast and even if a PU Software indeed needs much more maps and lines of code (at least that's what I think), it's still super fast.
ECU Software is indeed a core element, while you have the ECU, you don't have "classic" maps which are changed and done. I'm sure, the Honda PU has at least 6-7 different maps (2 or 3 dimensional), if not even more, to control every aspect because everything has to work. They also have to code all the algorithms for switching valves and so on. It's like a car-ECU-remapping but 100000x more complex
In the 2 weeks of time left to bring a new engine to melbourne, they could still put it new pistons, rods, or maybe even a whole cylinder head. For these Things you could calculate a manufacturing time of maybe 2-5 days, everything is build together in one day and the rest is breaking in for maybe one or two days, then it can be shipped.
Honda has the ressources to do things this fast (like every other PU manufacturer). If they have a CAD-file ready, which is safe to go, the time to track is low. The only thing is, that the parts wouldn't be tested well.
All in all: If Honda wants to bring a new part to the engine, the 2-3 weeks time from creating/modifying the part to a engine at track is much lower than you may expect