My idea for such a circuit would be to put the screen at B+ voltage
and use the grid and cathode for the oscillator (screen as plate
of oscillator, grounded-plate type circuit) Then modulate from
a low impedance source (i.e. speaker impedance) using a
plate transformer in reverse to plate modulate the tube. Gain
would be adjusted using a say 25 ohm wirewound pot before
the primary of the modulation transformer.
the basic idea is at
http://nmwilliam.tripod.com/el84.html
though this uses a crystal rather than a coil. However ...
that circuit generates several watts and needs watts of audio.