To do this I would use a 'blast from the past', a variometer.
This consists of two coils, one fixed and one rotating inside
the fixed coil. If both are the same inductance (so the outer
one is would with wider spacing than the inner) when they are
in "series aiding" the total inductance will be the sum, plus
the mutal inductance. When they are series opposing, the total
inductance will approace zero. (over simplifcation).
Variometers have NO moving contacts so they are easier to build
than rotary coils. They can't be made as large in inductance
without avoiding other problems (large distributed capacitance),
but a small variometer in series with a multitapped coil is a
good compromise.
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There's a serious shortcoming with variometers for transmitting purposes.

As the inductance reduces the wire resistance remains constant.

Result - extremely low Q for small inductances.

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Reg, G4FGQ