It scares the hell out of me that everyday my wife and I are not able to defend ourselves when we drive to and from work.
I find it "scary" that you would even follow such a ridiculous policy in the first place. My company does say in their policy that employees can leave their firearms or other weapons in their vehicles but that they need to be properly secured and out of sight. They also have a posted sign on the entrance against weapons in the building. Of course they never do searches and with it being over 100 degrees outside, there is no reason I should not carry my gun in the building concealed (I have a CCW permit) and what they don't know doesn't hurt them. I consider my safety and my life above any government law or company policy.
Your company obviously has a more extreme policy as they don't even want guns in people's cars. Unless they are actually searching vehicles, I can't imagine why you would not bring your gun to work and at least leave in the car out of sight. Who cares if it is against their policy? They have no legal grounds to search your car and if consenting to have your car searched was a job requirement then you could just as easily park it on a nearby street or neighboring parking lot unowned by them. I would start carrying if I were you and just keep quiet about it.
I always find it a bit disturbing how some people are such "perfect citizens" that they will never ever break any law or rule or policy. While I don't advocate outright criminal destructive conduct, people need to make up their own minds in how they live their lives, regardless of what "laws" and "policies" others seem to think should fit everyone. Some laws are stupid and some are even destructive themselves. A law telling me I can't defend myself is a destructive law to my safety and even the safety of those around me, a law I will and do not follow.