iPhone6 buggy, slow since iOS11, bad experience at Apple store, what to do?

Hi everyone, seeking guidance for the following situation:

After I updated my iPhone 6 to iOS11 I have had a number of issues including:

-Lag and delays (up to a few seconds), consistently inhibits typing, camera, general phone usage/navigation.

-Texts are out of order (e.g., I text someone, then their reply appears above my message).

-Phone has shut down a few times when outdoors in winter weather. Never experienced this before.

I have gone through most threads related to these issues, followed trouble-shooting steps, and have not had any luck. The phone is ~3 years old, 35 / 128 Gb available, AT&T, version 11.2.5 (15D60).

I scheduled an appointment for the $29 battery replacement at an Apple store in NYC. When I brought the phone in, an employee ran diagnostics and did a visual inspection, and said the battery replacement would be done in 1.5 hours.

When I returned, I was told that the internal liquid contact indicator (LCI) was tripped, so Apple could not replace the battery. I have never seen any signs of water damage before tonight, and (for what it's worth) physical/water damage has never been an issue in 9 years of using an iPhone.

I was offered a refurbished iPhone 6 for $299, but I opted to keep my current phone. Unfortunately, there is now a faint blue splotch under my screen that to my knowledge was not there before.

Please note I am not accusing or blaming Apple or any employees of anything. All my interactions with Apple's staff were friendly and professional, and I fully understand Apple's policies regarding the LCI and battery replacement. In 9 years I have never had to seek Apple's help regarding an iPhone issue, and I am wondering if there's anything I can do that might lead to a less unfortunate outcome. Is it worth taking the phone back and explaining everything? Any advice appreciated.

Thanks!