Anyway it was a good experience to go thru the process. So anyone reading this long and boring thread, do not plan to get to the station with less than 20mile range remaining in the bitter cold(below 20) as he will shut himself down at any moment.
And after the incident, I've lost 10miles of range.
But I'm thinking I got nobody to blame but myself for letting the battery deplete completely, probable cause of battery weakening.
For informational purposes, I have ran the battery down to 1 or 2 miles left without a problem during summer weather days.
Also roadside assistance confirmed that they will cover the towing bill.
This is not surprising that you lost 10 miles of range. It's pretty clear that your BMS calibration was significantly off. I know it's anathema to many on here, but I always feel better discharging my car all the way to shut down at least once a year to recalibrate my range. I've never had my cars (3 Model S's) shut off before 0, and I drive my cars down to single digits regularly, warm, cold, hot, freezing weather.
It's my opinion that if you don't do this, you'll get in a situation like you describe where it shows remaining range, but it's really just not there. I'd much rather face potential accelerated degradation an unspecified number of years down the road than be stranded on the highway in the freezing cold for 2 hours. Besides, I don't believe that a once or twice a year complete battery discharge/recharge cycle is going to materially affect the battery in any meaningful way.
What it MIGHT do is show defects in the battery sooner, which is fine by me. I'd rather have a pack completely fail during one of these cycles because it's being treated rough, than crap out on me when I'm NOT somewhere comfortably charging my vehicle.