I thought about it some the last few days and finally solved the problem.. I'm posting it for completeness. I appreciate everyone's replies, some of you were kind of close and beating around the bush.
On Step 20 of the iPhone 6 Lightning/Headphone Connector Assembly Replacement Guide, the following connector, that I circled in red, connects the whole lightning connector, headphone jack, noise cancelling mic, vibrator, etc that I previously replaced. This is the last easily known point that that the headphone jack connects into the main logic board. I just needed to clean this connector several times well with 91% IPA and some qtips and picks, then put back everything together. All of the headphone issues are now resolved.
Some water must have gotten onto this connector, dried, and bridged the small contacts with mineral residue. Even though I previously cleaned the whole board, I must have missed this. I now probably have a good spare lightning connector/headphone jack assembly.
Anyways, thanks to everyone (and in the related post) for getting me thinking in the right direction. Hope this will help someone in the future.