6s battery replacement

I have an iPhone 6s in excellent condition, but needs a new battery. The battery discharges rapidly, and sometimes goes from 90% to 2% like instantly, then the phone reboots. So I made an appointment at Best Buy. The phone is not in any kind of warranty, but i was ok with paying the $50 cost of the replacement. The Geek counter tech plugs the phone into his computer, confirms the numbers with Apple, then Apple runs an on-line battery test. While we stood there and watched the battery % slowly drop, 1% at a time, and the back of the case getting warm to the touch, the tech says sorry, Apple will not allow the repair, they say the battery is ok. I made sure they understood I was expecting to pay for the replacement, but he said the battery was testing At 87%, and that it couldn’t be replaced until it tested under 85%. He said I might be able to take it to the counter at an Apple store, and they might do the repair, but the nearest Apple store is 60 miles away, I am 83 years old, and just can’t commit to that kind of trip in the middle of a Colorado winter. He suggested an Un-authorized repair station, but that could lead to other issues in the future. We have a local store called Batteries Plus that replaces phone batteries, but I have seen the results of some of their work, and it’s not pretty. Any suggestions??