2001 Prius large battery failure

I have 2001 Prius with ~84K miles. I’ve had some bad luck (and some good luck) since owning it. About two years into owning it, the death triangle came on. The dealership kept the car for 6 weeks. They eventually found the problem (I can’t remember what it was, though) at no cost to me. Last year, I got the death triangle and turtle. The transaxle had gone bad just out of warranty. Toyota replaced the part at no cost to me. Now, I have the death triangle and the check engine light. I took my car to the shop today and was told that the large batteries are failing. The cost will be $3500. The warranty for the batteries is 8 years or 100,000 miles. While the 8 years have passed, I’m not near 100,000 (especially for such an old car).

Everything I’ve read in these forums has said that most people encounter this problem around 140K miles.

1. Could there be another cause?

2. Is it possible to upgrade the battery to the kind that was installed in the 2004 and on models?

3. Is there something I can say that would convince Toyota to pay for the repair?

4. What questions do I need to make sure I ask when I go to the dealership next?

Thanks in advance for your help.