The defrost thing is a shot in the dark but ill leave my explination for if im correct or not in the morning

obviously dont drive without heat and do not drive with ur windows foggy... but should be ok for a short test....
I have a few theorys and nothing has to do with reverse. 2way may beable to chime in on that i dont dive into ecu and wiring much, but what i want to know mostly has to do with sensor data, for example when its cold, is your maf sensor reading currectly or does your car think its a drasticly different temp then it is outside.
Example: if its 15deg outside and one of your temp sensors reads -40f it will behave very differently when there is a load placed on it expecially being in reverse your most likely not pressing the accelerator but gently easing off the brake.
Obviously this may not be the case but sensor data during diag is VERY helpful. Could have somthing to do with your cat being clogged, or O2 sensor malfunctioning while its cold or a bunch of things similar to that.
2000 GTS Turbo