I'd recommend a down conversion architecture over a set of filter banks. For example, use the ADF4351 as a swept LO from 1.03GHz to 1.25GHz to down-convert a fixed-frequency 1GHz sine wave. I'd generate the 1GHz RF with a 2nd PLL and a narrow band-pass filter. Finally clean up the 30-250MHz IF with an appropriate low-pass filter. The worst case mixing product you'll need to worry about will be sitting all the way above 2 GHz.
With the ADF4351 this approach has the drawback that the chip would have to run with a significantly lower amount of output division, which means higher phase noise: every division by two will lower the phase noise by about 6 dB, given that the divider does not add any phase noise. The second PLL will also contribute phase noise. If this is critical in the application, I would prefer a harmonic filter bank with the ADF4351. And I would use solid state RF switches rather than relays, as others have already remarked.
I was just wondering if this sounds like a sane design choice and if this is the 'commonly' used method of filtering out harmonics.
There is nothing wrong with a filter bank. But you should carefully asses the amount of LO harmonics you can tolerate with your PA and modulator, and make design choices accordingly. When you are using a class C or E output amplifier, the requirements may be different than with a linear amplifier.
Also, the ADF4351 is rated for output frequencies from 35 MHz to 4.4 GHz. I'm not sure if you will get it to run at 30 MHz when you want to use its output directly without down conversion or further division.