Hi Kostas

I could not resist inhaling some more lead solder fumes. So I went to my lab and replicated your circuit, except that I use a J310. 

In my opinion it is very clear that your circuit works. I put two random junkbox crystals in the circuit. 3.579MHz, 5.9904MHz. I can see on the oscilloscope that at some trimmer settings one crystal oscillates, at other settings the other crystal oscillates. At some settings the screen became a messy waveform and it is necessary to consult the spectrum analyser. 

My spectrum analyser has a 50-ohm input. I had to build a common-collector buffer. This adds some distortion. But now I can clearly observe together, the 3.579MHz peak and the 5.9904MHz peak. 

Kostas, this result is easy to obtain, I do not know why those forum people said it does not work. Mine works easily. 

I will get some 'scope screenshots and spectrum analyser shots for you. I will try 3 crystals also.

73 Hans G0UPL