(8) A loaded or unloaded firearm or other deadly weapon shall not be deemed
concealed on or about the person if it is located in any enclosed container,
compartment, or storage space installed as original equipment in a motor vehicle by
its manufacturer, including but not limited to a glove compartment, center console,
or seat pocket, regardless of whether said enclosed container, storage space, or
compartment is locked, unlocked, or does not have a locking mechanism. No person
or organization, public or private, shall prohibit a person from keeping a loaded or
unloaded firearm or ammunition, or both, or other deadly weapon in a vehicle in
accordance with the provisions of this subsection. Any attempt by a person or
organization, public or private, to violate the provisions of this subsection may be
the subject of an action for appropriate relief or for damages in a Circuit Court or
District Court of competent jurisdiction. This subsection shall not apply to any
person prohibited from possessing a firearm pursuant to KRS 527.040.

Quoted:
AFAIK there's no such thing as a provision for "only hunting weapons" or "only unloaded".

Also this could be rather interesting because of this case: https://www.frostbrowntodd.com/resources-Kentucky-Court-Okays-Employer-Weapons-Policy.html

TL;DR version - employee was disciplined because he had a rifle in his car in plain view but didn't fill out the company-required "weapons approval form".  The court sided with the employer because firearms were *not* actually prohibited, and because the firearm was not concealed.

In your case however, firearms ARE being prohibited - by limiting what kinds you can possess in your vehicle.  I also personally feel the "unloaded only" is a violation but SP has a stronger grasp on the law in KY of course.

In any rate it may be worth taking the company policy to a lawyer.