We have shotguns, but no one carries them. Those who do carry a shotgun in their car carry their personal guns. All officers supply their own sidearms, magazines, ammunition, cuffs, etc...the only thing we are issued is a uniform, brass, and a Taser.
The only other viable option i the Nova. However, I strongly urge you to get an 870. They work, and they work well. As for your 3.5" desire, I don't grasp that one. My personal 870 wears a 2.75" only barrel, and that has never been a requirement. I can not think of a SINGLE scenario where a 3", let alone a 3.5", shell would be required, or even desired.