There is a big difference between the mvam 2 and the bb510, the mvam 2 is 20 to 40 pf, the bb510 is 20 to 440pf.
That said the circuit works well with a 20 - 500pf airspaced variable cap, and a 10 - 365pf polyvaricon.
Do you think the o/p waveform is tuning the diodes and killing oscillation?
I dont have any mvam 2's, but I tried a couple of leds reversed biased as varicaps (the ground side one lights up), and I had the airspace cap in parallel too, it worked, but obviously there is very little tuning range from the 'varicap leds' like this.
Yes I tried reversing the lower diode, after all dual varicaps are often common cathode, but that didnt work either.
I was thinking of putting a largeish cap (0.01u) between the lower diode and ground, but if I did that there would be no dc path to ground for the diode bias voltage.
I'm thinking the Q of the tank is probably on the low side with the high - pf varicaps (I wonder if the 100k on the tuning voltage line is effectivly shunting the tank), and better just to the point where it works with the airspaced caps.