There's not a great deal to the existing I/O board. We can deduce from various documented pinouts for the RJ45 connector what the two RJ10 connectors do. And obviously we know what the DC jack does.
Cor blimey, those two power lines are awfully close! Not sure I'd trust a cheap high volume fab house with that sort of spacing (especially if they're the ones who soldered the DC socket on wonky...). Pins 3 and 4 of CON2 (middle left) are a bit mysterious - but I highly suspect they're RTS/CTS. We don't really need them - they may just be there for factory programming or debugging or testing or something. If you check out the main board, it doesn't look like they go anywhere...(photo purloined from Jack Kelly here). I guess the track might be on the other side, but I don't fancy dismantling my display if I don't need to!
Anyway, we can extract a schematic
Groundbreaking stuff, right?
The challenge will be finding a way to fit the ESP-12 onto the new board without it interfering with the required connectors. The internal RJ10 connections can be moved around a bit (possibly even off the board entirely with a breakout if needed, although that would require another board so I'd rather avoid that), and we might be able to get surface mount versions of these connectors to make a hole free space (although the retaining posts might be problematic).
Ideally, I want my board to be a drop in replacement - so I want to avoid changing the connectors if I can. Whilst it may be easier to change those RJ10's for pin headers, that makes it more difficult to install on a unmodded unit.