I have an extension cabinet with a single 16 ohm 12" speaker.
Of course, all of the amps I want to use it with only have an 8 ohm output.
Without introducing more speakers, what would be the best way to knock the resistance down to the cabinet?
Agree with hank57, most amps can handle a speaker that has a resistance one step higher than the resistance rating on the amps tap. Depends on the amp though. Going to a lower resistance speaker is where it gets more dangerous.
You'll limit your maximum power to the speaker having it work into a mismatch. In solid state amp's you can predict it as a halving of power. In tube amps it could be a little more or less than half. In your case I doubt the output tubes will mind working into a higher impedance load.