I'm not sure I follow your logic. You're happy to pay for HEx/taxi (at ten times the cost of the Piccadilly line) for no noticeable time saving, but then you're trying to save a tenner on the SouthEastern ticket?
In any case, I'd never advise an "advance" rail ticket after a flight - as it has zero flexibility yet you can't guarantee the exact time you'll get to the station, so a high chance you're either hanging around or (if late) you're ticket is worthless. I would just walk to the ticket window at St Pancras, and they'll sell you the cheapest available walk up ticket (which will vary by time of day, peak/off peak rules).