Interestingly, the resulting text file shows ~130 lines for the period between 2012 and 2014, and then ~1000 lines for the period in the last couple of days when I've been poking around with the old wallet.dat file, trying to figure out what to do.
In the past, Bitcoin-qt only created a new private key when it needed one. At some point (and I'm not sure what year) it was upgraded to generate 100 and later 1000 addresses "keypoolsize" upfront, so an older backup wouldn't instantly be outdated.
My guess is those 1000 recently generated keys were meant for this.
That being said: if your current wallet.dat came from a different backup than the latest version you've actually used in 2012-2014, it might not include all your private keys.
And in case you're still going to make any transactions from this wallet.dat: you should make another backup (don't overwrite older backups), because those 1000 addresses are probably not included in your previous backup.
about half a bitcoin.
For future recovery: your half a Bitcoin has
about $300 worth of Forkcoins. Don't bother about them now, and don't try to recover them before securely moving out all your Bitcoins, but don't forget about them either.
Of the ~1000 recent lines generated by 'dumpwallet', I did a test of the first 50 to see if anything could be swept from those wallet keys. No dice. Electrum returns a 'No inputs found' message.
That does make sense if the addresses were only created recently.
What do you think is causing Bitcoin Core to show that available balance? Is it "confused" or caught up in a transaction history that... just doesn't exist?
Suggestion: turn on Coin Control in Bitcoin Core's settings. Then click "Send" > "Inputs" and see which address holds that balance according to Bitcoin Core. Check that address on a Block explorer.