Well, I posted this question, now I think I have found a good answer to it.
If you look in the code for Net_Gearman_Worker, you'll find that in the work loop, the function stopWork is monitored, and if it returns true, it exits the function.
I did the following:
Using memcache, I created a cached value, gearman_restarttime, and I use a separate script to set that to the current timestamp whenever I update the site. (I used Memcache, but this could be stored anywhere--a database, a file, or anything).
I extended the Worker class to be, essentially, Net_Gearman_Worker_Foo, and had all of my workers instantiate that. In the Foo class, I overrode the stopWork function to do the following: first, it checks gearman_restarttime; the first time through, it saves the value in a global variable. From then on, each time through, it compares the cached value to the global. If it has changed, the stopWork returns true, and the worker quits. A cron checks every minute to see if each worker is still running, and restarts any worker that has quit.
It may be worth putting a timer in stopWork as well, and checking the cache only once every x minutes. In our case, Memcache is fast enough that checking the value each time doesn't seem to be a problem, but if you are using some other system to store off the current timestamp, checking less often would be better.