What does it being 2 years later have to do with anything? There is no time limit. Heck, they could drop the claim tomorrow and put it back on next week.
If it's their music (something you haven't denied), then be grateful you were able to steal from them for that time and nearly 1 million views.
Considering it's not a copyright strike and only a 3rd party claim, I fail to see what the problem is. It's their music, they deserve to be paid for it.
That all said, I find it hilarious that you're willing to delete the video and start over from scratch just to avoid paying what they're due... especially when it's clearly your most popular video and likely brings traffic to the rest of your channel. But, that's your call- just realize that the same video re-uploaded with different music will (most likely) be viewed far, far less than the one that's currently up there- even with identical tags, description, and the like. At nearly 1 million views, it's earned it's spot in the algorithms and it pushed appropriately by YouTube. A new video would have to start that from scratch... and would be buried in the rankings until / if it ever catches up.