I've been trying to remember the details on a gin rummy game I played when I was younger. This game had the last round require a "run of seven" and a set of three. Looking at Wikipedia I see Contract Rummy which is similar but doesn't have this requirement for the last round. Does anyone know what flavor of rummy was represented by this type of last round?
Sounds like you've already found the answer: it's a form of contract rummy, just with a different final contract than the one listed on the Wiki entry.
From the contract rummy entry on rummy-games.com :
The rules detailed below are representative of all Contract Rummy games, though there are numerous regional and local variations even among games with the same name.
Incidentally, that particular contract (7+3) appears as one of the contracts in Shanghai Rummy (but not the last).