Haven’t seen this issue myself, but I don’t use a car battery. I personally use a car battery charger.
I have also used purpose built embedding tools which heat spikes which are then pressed against the wax and wire. These may give you more control over the heat applied. They recommend using 12v battery or car battery charger.
Speaking to someone at the club last week they mentioned a heated embedder tool which looks like a soldering iron with a spur wheel on the end. This isn't something I have used, but a tool they highly recommended. These can be found on eBay (sorry, can't recommend a specific seller):
Lastly, you could use a spur wheel embedder. When using these, I would recommend an embedding board to sit inside the frame under the wires to push the wires on to. I personally haven't had the best experience with them as I find the heat when the frame is placed in the hive often undoes the work of the spur wheel, with the wax falling off the wires.