Keeping a paper trail
Good records are the single most useful tool in any appliance warranty claim problem. They turn "he said, she said" into facts you can point to.
Use one folder
Keep a paper folder or one digital folder for this issue only. Put every bill, letter, receipt and screenshot in it, named with the date first so it sorts in order.
Write things down the same day
After every phone call, write the date, time, the person's name, what they said and what happens next. Notes made the same day are much more believable than memories weeks later.
Prefer writing over talking
When something important is agreed on the phone, send a short email that says "To confirm our call today..." and repeat the key points. That creates a record the other side can correct if they disagree.
Take photos and screenshots
Photos show condition and dates. Screenshots capture web pages, prices and account screens that may change later.