I personally wouldn't run them. I know others swear by spacers, but you have to check the toque more often, or should at least. Also I don't trust the flatness of some spacers.
You seem to be a young guy that's pretty smart. One bit of advice I'd love to give a young man 10+ years my junior: focus on your career until you're at least 25. That's not to say don't have fun, but the next 10 years of your life can really accelerate the following 20 if you plan it right...
Yeah "recharging" the battery isn't as simple as the dealer was making it out to be. If it ever said to "replace battery" on the dash, it needed to be replaced. But the BMW system registers the charge of the battery and then it plots the voltage decline and the rest of the computers compensate...
So even after the cold start and you put it in park, it has the delay? I'd keep an eye on it. Maybe it'll just go away.
I'm guessing it shifts fine in auto and manual mode, in sport and comfort?
When I park my car and pop the trunk, it'll re-latch when I close my driver door. Car is still unlocked. Being able to get out of the car, close the door and then press the trunk button would be great.
Right now, I have to get out, leave the driver's door open, open the trunk, close the trunk...
Targa is the only thing that would make the Supra perfect for me. I'd be afraid of the price. But thankfully these cars basically don't depreciate so I could jump into the targa without taking a loss.