I get that, I am rubbish at pushing BT too....and then complain about the early starts
To be honest I'm not sure what I'd have done. With DD I would have let her sleep as she was never a car sleeper, if she dropped off it meant she was totally exhausted and probably needed it. DS is different, he sleeps in the car far more easily. So I'd probably have woken as you did to try to preserve the later nap. I do that quite a bit right now (we are in 2-1 territory) if he wakes too early to make a lunchtime nap, quick 15 mins CN in the car doesn't seem to alter how he goes down at lunchtime. Either way it looks like your day was ok. How was the night?