You are quite correct Transport Mode is activated when the battery becomes depleted, it shuts off the blower speeds, heated rear screen and AC in order to conserve what power remains in the battery for starting the car. It should have been deleted during PDI at the dealers when they sold the car but they don't do it. Probably a money making scam as they would charge a diagnostic fee and just reset it to Normal mode to the less knowledgable owners.
With the correct software its very simple to reset it, I use BMW Scanner 1.4 to reest Transport mode, itr lives under the Aircon menu, always best to clear any codes it may have set whilst doing the reset as well. As soon as its reset you will hear the aircon fans spring to life as well as the heated rear screen being restored. BMW Scanner is cheap to obtain and set up on an old laptop running Windows 7 or XP.
I do have a Creator 310+ handheld scanner that shows Transport Mode in its menu but the function dosn't work when selected, may become functional on future software updates, think its on version 12.1 at the moment, it was shipped when new with version 11.9.
BMW Scanner 1.4 can be sourced on ebay for little outlay, its really useful and simple to use.
Have reset a few Z4's for members near me, shame you are so far away coud have done yours.
As to deleting Transport mode following the info on here and Youtube have tried delting it using NCS Expert, Winkpf and Dis which are the software in the BMW INPA packages also on ebay. Not had any success in deleting it using any of these so far.