The current step is designing a filter which will limit the levels of unwanted tones, but only to an extent that allows for a reasonably strong signal in the passband so that the CMX901 PA receives a reasonably optimal input power, and touch up the signal after it has been amplified. I have been experimenting with different implementations of such a filter in Keysight's ADS; I am currently looking at using a notch filter to reduce the ~105 MHz signal from the mixer (which is equally strong as the desired 144.39 MHz signal) and a high-pass filter to limit any other tones that might be present:

This has what appears to be an acceptable response, as simulated with MuRata components:

However, the next step will be to measure another FFT from the actual board at the output of the RF mixer, which is data I have observed but not captured since modifying the LO signal amplification. With this data, it will be easier to design the most appropriate filter.