The term used in "Pistol Free Zones" is "premises." The only exceptions to this is in the CPL law that exempts parking lots (except schools) and there appears to be no exception for those without a CPL. This is discussed in great detail many places and no firm, definitive answer could be found by me, only speculation as to how you could get around it in a court of law. My opinion would be that the parking lot of the grocery store would not be legal for you to open carry in.
My next thought though, is that the fireworks company has leased a portion of the parking lot. One could argue that the fireworks tent is its own business and has its own parking areas directly around the tent, and that the fireworks company has not liquor license. If it was me I would ask the owner of the fireworks business if you have permission to conceal carry, and then conceal carry on his business property that he is leasing. I think this would be your safest bet.
If you do not wish to ask permission, nor take a chance, locked in a case with the ammo separately stored may be your best bet. I am confident folks more well versed in the law will chime in soon, and you may get better guidance yet I hope. Personally, I would open carry on the grounds that you are on the fireworks company's property and parking lot and not the grocery stores. I feel that is a solid fact if it ever went to court.
