iPhone 6s charging to 1% and cycling restarts after 1-2 minutes of use.

I purchased an iPhone 6s refurbished from a 3rd party about three months ago. I had no problems with it until about 2 weeks ago. It died at ~20%, which it had never done before and upon being plugged in, immediately displayed the apple symbol, before turning on it would cycle again as if resetting. After this cycled for about an hour i eventually got the phone to turn on, only to have it restart after about a minute or two.

I went through the laundry list of software fixes: multiple hard restarts, restoring the phone to factory settings; through the phone and plugged into a computer, logging in through secure mode on the computer to attempt a diagnosis, restoring the phone from a few month old backup and updating the ios software. All of which was extremely difficult to accomplish in my 2 minute timeframe of the phone being on.

Finally brought it into the apple store to see if they could diagnose the battery or hardware failure. While there i couldnt get the phone to get past the phase of restarting before even turning on. When she plugged it in and finally was able to activate the secure mode, in order to attempt a diagnostic, it failed and she declared there was nothing they could do and asked if i wanted to replace it for $300. I declined and went home. After finally getting the phone on and active i retried many of the steps i had tried previously, and then gave up and activated an old phone for the time being.

After leaving the phone dead for a few days, i decided id plug it in and leave it overnight (which i had also attempted before activating the new phone) to see what happened. Low and behold when i checked it the next day it had fully charged, i left it plugged in for a day and then took it off to see if it would hold. It did and has cycled charging and holding a charge for a few days now.

I decided to bring it in to the apple store again to see if they could further diagnose it now that it would stay on. She ran some test holding her ipad up to it and said it was receiving a panic failure notification everytime it was restarting and that this was a logic board failure and i could replace it for $300... again dissapointed i attempted to pry and find out what was actually wrong. She did a screen test and said it was 3rd party and that that could cause the failure, or since i bought it refurbished that the battery could be 3rd party and this could be the problem but she couldnt tell without opening it up. Im now sitting in the parking lot trying to get more answers, is there any further way to more completely diagnose the problem? If its the third party battery or screen i would much rather have those replaced officially than buy a whole new phone, but i dont want to go ahead on that if i dont know for sure, also, who would i go to for something like this? Would i have to go through an apple store? Or would i be better off finding an apple recognized service center at a best buy, or going third party again. Im trying to be as economical as possible while still maintaining a phone that wont shut off on me randomely. Thanks for any advice!

-Ben

Additional details: during its reset cycles, occasionally it would display 100% or 2% battery rather than 1. Also, i noticed on occasion, if i opened an app when it turned on and then left it plugged in it would sometimes refrain from restarting if i wasnt using it for up to maybe an hour or more, evidenced by the app still being open. But other times it had obviously restarted.

Also, the phone has received no damage, no significant drops or screen damage or water damage, which she checked for.