Yes, a bipolar transistor will be the low risk choice for mass production. I'd still prefer to make a JFET VFO/VCO for a one off homebrew design though...
Some people have claimed great success using a Vackar circuit using a JFET (or a bipolar) device so maybe the OP could google for this?
Because the OP's original circuit locks the varactor bias at 0V I think the RF waveform will explore the region towards forward bias on part of the waveform.
I think the diode will then begin to resemble a very non linear capacitor and the capacitance will increase a lot towards the (negative) waveform peak. So this will be what pushes the frequency down. So I think the tuning mechanism for the original circuit will come from tuning the damping resistance via the emitter follower. The waveform won't have to get fully towards forward bias to give the 'tuning effect' and so it won't be obvious (on a scope) what is actually happening in the circuit.
For this reason I'd expect the OP's circuit to be very sensitive to temperature changes so this is another reason the design is poor. It would probably 'tune' if you forgot about applying a tuning voltage and removed the emitter follower (and the associated bias voltage) and simply replaced the 1k resistor with a passive trimmer resistor to ground. I suspect that you wouldn't have to change the resistance very much to see the frequency change by the required 40kHz. See the image below.
I wouldn't recommend anyone to make/build the circuit below because it will be just as poor as the original circuit. The circuit below is not a good one