The feedback problem is because in order to work at both frequencies the stage has to be linear. The RF signal would have to sit on top of the lower AF signal as they pass together through the transistor. When oscillation occurs, the transistor will be driven in and out of conduction so the other signal will become chopped up.
If you try it, bear in mind that the phase of the audio transformer has to be correct to give positive feedback, it may be necessary to reverse one of the windings to make it work.
My point about not being tunable is that the receive frequency is fixed by the crystal so CW signals nearby to it will have different audio pitch depending on their exact relationship to the crystal frequency. If you narrow the audio passband you will start to lose signals away from the audio peaking frequency so you will only be able to pick up transmissions in a very narrow range of frequencies. For example, if the crystal was (example) 10MHz, the audio peaked at 1KHz you would hear a CW transmission at 9.999KHz and 10.001KHz only, any other frequencies would not be heard. Holding a two way QSO would be difficult as each station would have to transmit exactly 1KHz apart.
Brian.