Forget it, you're wasting your time. The Home Warranty company already has it in their computers that your furnace rusted out - they will not pay off, ever. This is why I stopped doing home warranty work, they look for each and every excuse to deny your claim.
At this point, it's a lost battle. You can argue with them until you're blue in the face, and if you bother with a lawyer to make them pay you'll end up losing money. Get some bids from a reputable heating contractor and get that sucker replaced.
Sorry, man, you lost.
"We always fix it right the second time".
All posts are strictly my opinions and not those of my employer. I cannot make statements on behalf of my employer.
All advice posted by me is for educational purposes only, HVAC repairs should only be conducted by trained & qualified people.