Thanks for posting. I understand your concern. I can confirm that if you were to remove the battery from your speaker, it would void the warranty. Your best bet if you have a problem would be to contact your local support team for assistance. Here is a link you can use. Click on your region, scroll down until you see "Contact Us."
I don't work for Bose but here is my personal take:
1. All the Soundlink Minis (1,2,3) according to Bose are discontinued
2. Many Minis seem to have the yellow light problem but not all and I have not personally read anything suggesting a cause (though I have not read it all). I have a Soundlink Mini 2 and it does not currently have that issue
3. It is unlikely you will convince Bose to repair it for free but you can try.
4. Bose no longer (according to the last time I asked) exchanges Minis for Minis. They offer an upgrade to a Revolve for $220 (absurd imho).
5. $80 seems like a fair price - perhaps you can convince them to exchange / replace the battery as well for the same price. I would not pay $80 for repair and another $80 for a battery since...
6. A new Mini 2 on eBay or Amazon is about $160 (though we do not know if those will end up yellow lighting as well).
7. I am not personally convinced that the battery has nothing to do with the problem.