Please note that FDTD and other Lumerical products have a dedicated forum in Photonics: Photonics (ansys.com)
imporper location can cause delay of reply.
not long enough simulation time can reduce the sharpness of the resonance. However, the absolute transmission might not be so important as you know for extremly high Q it can be challenge. In that case, you ca simply simulate it to autoshutoff min to 1e-7 or smaller. As long as the result is smooth, it should be ok.
The other viable method might be worth of trying is: simulate the Fresnel coefficients or S parameters of the mirrors and use the cavity formula to get the tranmission. This of cause will depend on the device you simulate. If there is only one mode, this method should be accurate.
Unfortubnately we do not have subscription to the paper you refer to.