Is it possible to construct a custom transaction in which either your key, or the key of an "overseer" can spend the coins?
Yes. That would be a "1 of 2 signatures required" multisignature transaction.
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And add a feature such that all subsequent transactions you make also have to include the overseer's override feature?
That you can't do. If the coins were stolen, the thief can just sign them away.I suppose you could do a "2 of 2 signatures required" and then have the overseer only approve transactions that were ALSO 2-of-2 required (where 1 was the overseer's signature). A thief could take your coins away, but wouldn't be able to spend them without the overseer's OK. The overseer wouldn't be able to take them back, though.
More complicated schemes are probably possible if you want to trust the overseer completely... but if you and the person you are paying trust the overseer completely then why bother using bitcoin transactions at all? Just hold accounts at the overseer and they can transfer balances or reverse transactions as they like....