So a motherboard replacement did fix the issue - for $35 and some work I'm happy. I nearly succeeded in cleaning the motherboard (there was some salt deposits on it - presumably from the water), but dislodged an SMT resistor in the process. No reflow oven means :( UPDATE (1/17/18) - Phone was getting pretty hot for a while and then developed the same problem. Moving on to a different phone at this point. I suspect maybe the charging circuitry or battery have problems.
I'm not familiar with that specific connector but its likely it will be the same style as the ones in this video: https://youtu.be/lrs8-KtJGus?t=56 You might inspect the old, busted, connector to get an idea of how it releases. Some different connectors have the wire come out the front of the connector. I've seen people use hair pins and skinny screwdrivers to get the 'primary locks' released.