re: How should this dispute with a furniture store be handled?

I work in the corporate office of a furniture company. I guarantee you signed something that released the store from liability. Now, if the store was worth a shite, they would replace your chair and either write-off your loss, or (if they do enough volume in sales) tell the manufacturer it was damaged and have them part it out.
But, if you went to some nickel and dime place that has good prices then you're probably just fricked since they can't take the hit monitarily to replace the chair and eat the cost of trashing the one you willfully drove off the lot with.
Moral of the story: bring your own tie down straps like a real man. I'm always surprised when I'm at our stores that people will tie up a $5k couch with the little nylon string we have and think that's sufficient.