First of all, if you get in an accident because your phone is not connecting through BT, that's on you.
Nothing you do, whether using a phone for maps or for entertainment, should ever distract you from driving, and if it does, you should power your phone off and put it away until you reach your destination.
That may sound harsh, but it's an accurate depiction of any driver's responsibility, the same as if someone said they got into an accident because the song on the radio was just too good and they were distracted.
Second, as there is no command any BT device can send a radio to make it reboot. If the radio is crashing and rebooting it's a bug in the radio, and the radio's manufacturer (usually an OEM like JVC) will need to fix it. I have no idea what Toyota's policies are for providing updates to their infotainment system are, but only they can fix it, presumably as a warranty item.
Believe it or not, despite their market penetration, there is little Apple can do to force any auto maker to update their systems to fix a bug on their end, and even today auto makers are not used to having to make or distribute software updates.
You have worked with Apple Support directly, so make sure they are fully aware of what actions you have and have not taken with Toyota.
That information should get passed on to Engineering; of course it never hurts to file a summary here as feedback as well:
Feedback - iPhone - Apple