The latest firmware for your drive on the LG Electonics US site is version 1.03, although there are v1.04 versions at non-LG sites.
If a firmware flash fails in a LG drive, the warranty is voided and they will not assume responsibility for the drive failure. Unlike Liteons, which can be recovered even if a firmware flash fails, with a LG you are sunk. See the LG policy at LG GCE-8400B Firmware
Personally, I would return the drive before flashing it if it is still under warranty. The drive replacement might hopefully contain the latest firmware (and especially if you request it).
Car CD players are notoriously of low quality and very picky about media. Some combinations work and some don't. Media using cyanine dye has a much wider range of sensitivity to laser power settings compared to pthalocyanine dye sensitivity. As writers and readers age, their calibration settings or power capability may change enough to push them into failure with certain combinations of media and hardware.
I would try using a cyanine dye based media such as Taiyo Yuden and see if this will work in your car player. This TY media is labeled as Fuji in the US and perhaps in other areas also.
Read the Media Compatibility With CD-RW Drives - Which Media Is Best?
for more information on media types and cyanine dye based media availability.