Andy Kunz answers me:
> I make a living driving these servos, believe it or not.
>
> Center on "new" Futaba servos (connector on servo is a female) is 1500uS,
> with other limits at 1000uS and 2000uS.  Don't know where he came up with
> 1520.

My servos are the "new" ones.

I must be misunderstanding how these servos are supposed to work.

Unless I've misinterpreted you, you're saying that the 1ms-2ms pulse
width range is where the servo has linear response.  I thought that it
was the whole range of the shaft (i.e. just over 180 degrees).  For my
application[*], I don't care too much about linear response, but I do
care about having a large range of motion.  Can I feed the servo my
over- and under-sized pulses, or do I have to add some gearing to avoid
harming the servo?

I also figured the "center" was the middle of the shaft's output range,
but you're saying that the center is wherever the shaft is when you're
feeding the servo 1500uS pulses (which, since the output is linear in
the 1000uS-2000uS range, is the midpoint of the linear range).

Thanks for the help,
Brian

[*] For what it's worth, my application is a camera platform with two
servos mounted at 90 degrees to each other (left-right and up-down).  I
can put the camera against a wall so that there's nothing behind it,
but I still want it to be able to look all the way to the left and
right, so I need a full 180 degree range of motion.