> oscillating +/- 1V

You want a P-JFET. Since your app is industrial you will have no troubles
finding one with low enough Vg0 (to be able to turn it off with 5V). You
want one with Vg0 of about 3V. There will be some parametric distortion of
the signal (which should appear as a higher 2nd harmonic in the output
imho) but it should work ok in your application. If for any reason this
makes the oscillator unstable then you have to change the feedback path to
attenuate higher frequencies more. But this is not likely to be needed.

Peter

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