The Reddit Apple's technician's suggestion comes from a well meaning place, but also a place of ignorance.
When you are an Apple technician, there are only four answers to any problem:
1. Restore the software
2. Replace the top assembly
3. Replace the battery
4. Replace the whole phone
The iPhone 6 top assembly includes about 8 parts that fasten together with screws (in this example, including all of the glued-together parts that make up the "screen" as one part). The top assembly also includes the home button and and the long flex cable which leads from the home button to the motherboard. Apple's technicians never take apart this top assembly. They consider the entire top half of the phone to be the "screen," including your home button and long home flex. So when you bring your phone to an Apple store with either a home button problem or a screen problem, they always change both together. This is also how earpiece speaker or front camera problem are fixed at Apple - by replacing the "screen." It's good in that Apple wants to ensure a high level of quality control though more new parts/less labor, but bad in that when you need a $2 speaker or $5 flex, the answer is a $149 "screen repair."
The Apple store is the only option if you want a new home button to include Touch ID. However, the independent store you brought to phone into has already tested a new button for its ability to click. You have already tested a new long home flex. As far as your issues are concerned, having Apple change the whole top assembly will accomplish no more than changing the home/home flex. You may want to visit one more independent that has both parts in stock, just in case a part new part caused this issue to be misdiagnosed. Find a local shop with good reviews that will not charge a diagnostic fee if they cannot fix it.
Beyond that, your problem would have to be caused by damage to the home button FPC Connector on the motherboard, or damage to the Touch ID circuit., meaning power is not being sent to your home button in the first place.