Someone on their end didn’t do their job. I would think a small discount is reasonable. This probably isn’t a huge corporation like a big hospital where you can offer a much lower cash settlement now and wipe the rest away.
I would call and inquire nicely. Tell your end of it. Holiday timing is bad and that isn’t your fault. See if they offer anything. If not I’d pay it off in 7-10 months just to be slightly irritating but that just satisfies you some because they clearly weren’t missing your $3300 so you paying $350 a month instead of $550 really won’t affect them because it’s still decent money coming in.
Why no insurance coverage? This has happened to us once on return from vacation and we just paid $500 and I can’t even fathom what the actual bill was. They were in our entire house for 2 weeks with 14 blowers running and removed and replaced carpet throughout 75% of the house.