A couple of points I would give here:
1) Your PWE results look like it is for a single defect. However, your design uses a L3 cavity. What exactly were you looking for in your PWE calculation? If it was simply the location of the bandgaps you should be doing the calculation over a pure crystal.
2) The gaps you are working with are well into a dense region of propagating states and gaps between them, it is difficult to sort out what wavelengths should work and which ones should not. This is made worse by this being a PWE result for a cavity which adds cavity modes to the propagating modes.
3) Typically in photonic crystal designs people work with the larger gaps, this for you would be the gaps from 0.18 to 0.24 (ignoring the resonator state in the middle). At this point I kind of need to ask what your design constraints are? Why did you choose 0.535? Are you able to change your lattice (a) and radius (r) values? scaling r and a to maintain your r/a value of 0.3 while lowering your a would shift the gap from 0.18-0.24 to higher values closer to your operating wavelength of 0.187.