Double Peak Phenomenon in Transimpedance Amplifier Simulation
The AD8014 data sheet clearly shows that you will get significant peaking of the output signal when you have a feedback resistor that is this low. I would be considering a resistance that is at least 100 ohms.


  If I increase the feedback resistance too high, the signal gets
  clipped, and I'm trying to avoid that.


At the moment with a 50 ohm feedback your peak signal is 900 mV. With 100 ohm it's going to be more like 1.8 volts so, given that the AD8014 is capable of producing \$\pm\$ 3.4 volts at its output, you should be OK. If the amplitude is too high for subsequent stages and causes clipping of those other stages then use a resistor attenuator after the front-end.