Continuously variable gain amplifier for a low distortion 1kHz Wein bridge sine wave generator.

We've been messing about using a FET as a variable resistor to try to control the amplitude of a 1kHz Wein bridge sine wave oscillator for months now.
It works, but it does introduce some harmonic content into the sine wave.
A good four quadrant analog multiplier can do a better job, but the AD734 isn't cheap. An asymmetric current mirror can do the job more cheaply but with even more components, and seems to introduce even more distortion - not all that much, but enough so that it isn't a good choice.
All we need is a controllable gain element that can adjust the gain around the Wein bridge to sustain oscillation at a constant amplitude despite component value drift with time and temperature.
Linear Technology and Burr-Brown both used to sell amplifiers where you could vary the gain continuously with a control voltage - I used both together in one project - the expensive Burr-Brown part managed the signal gain part, and the cheaper and slower Linear Technology part managed the DC offset feedback path.
The AD8330/1/2/6 parts all seem to do much the same job, as does the AD603. None of them are cheap, and the are all a lot faster than the job requires. Anybody know of anything more suitable?
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Bill Sloman, Sydney