Hi @gatewaynomad,
Okay, the three minute reset cycle is a vital clue as to what's going on. That's how often the iPhone scans its sensors. When it can't communicate with one of them, a catastrophic event called a kernel panic occurs, basically crashing the operating system and causing it to reboot.
The good part about this is that when those events happen, the phone logs them. You can go in afterward and read those logs and find out exactly what caused the reboot. User @flannelist has written up a very good Wiki article on those kernel panics that tells you how to read them and what they mean.
My suspicion is that the lightning connector flex cable you bought has a defective or missing sensor. There are two sensors on that flex assembly that commonly cause boot loops like you're experiencing. One is some kind of microphone sensor and the other is a pressure sensor used with the barometric vent.
[[iPhone Kernel Panics|iPhone Kernel Panics - iFixit|new_window=true]]
So your next step is to bring up your phone and go grab the panic log. Post a screenshot or copy/paste the contents to your question and we'll do our best to walk you through the solution. This is fixable, and signs are currently pointing to the replacement lightning connector assembly, but we'll know more once we see the panic logs.
Good luck, and let us know what you find!