Wien Bridge Oscillator
When I turn the preset and increase the gain to maybe 3.2 I still get
  stable oscillations, but larger Vpp and no clipping. Considering the
  Barkhausen criterion shouldn't the circuit render unstable, and the
  oscillations begin to clip?


Slew rate limiting is something to consider: -



Picture source

If your peak voltage is 10 volts (at 15 kHz) then the maximum rate of change is 0.94 volts per micro second. Given that the 741 self-limits at 0.5 volts per microsecond this is the likely cause of the output amplitude appearing reasonably stable with some distortion. You might see something like this at the output (blue): -



Picture source

As can be seen (in this exaggerated scenario), if the input sine wave (red) increased in amplitude, there would be no increase in the output amplitude. This is a form of output amplitude limiting. In your particular scenario, I suspect that the limiting is only marginal but enough to act as a form of amplitude stabilization.

Reasons not to use a 741 - maybe you have found a good reason to use a 741 op-amp?