...Are there simple fixes for reducing this single-coil hum?
You probably know that hum is worse if the single coil Jazz pickup gains are not set to the same level. Be sure your amp is plugged into a grounded outlet, stay away from the amp itself (like 10 feet), and keep the pickups facing away from the amp. Be sure your cable is shielded and in good condition.
Some of the hum may be due to EQ on your amp and tweeter setting, if you have a tweeter, though tweeters are more likely to hiss.
See if there are other appliances, i.e., neon lights, televisions, computers, fluorescent lights (including the new wine-cork type) operating nearby. They can also contribute hum. Essentially anything nearby with a strong magnetic field can be a problem.
In my area, there is a lot of radio frequency noise emitted by old and faulty powerline insulators. These actually seem to make the hum a lot worse from single coils in certain parts of my house. Try different locations to see if that helps. It did for me. I assume you have not opened the control cavity. If you have, you MAY have dislodged the bridge ground if you put much tension on the wiring. Note, it is not easy to dislodge this wire, but it can be done (I did it).
Finally, you can switch to split coil pickups, and even get the control cavity shielded. I like my Lindy Fralin Split coils, but they were not cheap, and they do sound different from single coils. If you love your tone as it, try some of the above.
