The BF256B has a too high tolerance for Ugs(off) which goes from -0.5 to -8V. That means that most of them will cut off below -4V. But the cut-off voltage should not exceed the half of the supply voltage (6V), thus only a cut off voltage of max. -3V is acceptable because otherwise the oscillators would not start and the demodulator stage would not output enough AF signal. That's why I clearly stated that you should use the BF256A.
Edit: The J210 should do the job, too, but not the J211 for the same reasons.
You may naturally buy about 100 units of the BF256B and build a test circuit to identify those whose Ugs(off) is smaller than -3V, but that's not very economic...