The reference you are linking to is fundamentally correct but it is a much simpler situation. Fundamentally what you have is a structure (photonic crystal) that does not allow propagation (band gaps) for specific wavelengths. This means that if you introduce a defect that has a resonant wavelength that is within the bandgap then light can exist within the cavity but cannot propagate outside of it due to the band gap. The location of the cavity/defect state (there is no band) is the location of a resonance, so at w/2pic of 2.11 you have a resonance, i.e. the resonant condition is met.
This is why your simulation did not work. What you likely chose was in fact a propagating band that existed between two separate band gaps and not a cavity state that existed in a band gap.
Also you are looking at finding cavity states using a structure with a single defect and then use that value in a structure with a L3 defect. The L3 defect will have a different resonant wavelength as it is longer, recall that a cavity length corresponds to the resonant wavelength. If you are going to use an L3 defect then use the PWEM on that structure and not the single defect.
As for the structure you are proposing, if the waveguide is within the evanescent region of the cavity and you excite the cavity then the light would enter the waveguide at resonance, I am uncertain why you think it would not.
I strongly encourage you to refresh yourself on the fundamentals of photonic crystals and designing structures within them. An excellent first stop is the book “Photonic Crystals: Molding the Flow of Light” by Joannopoulos, Meade, and Winn. If you can, get the second edition as I found it to have more information.