Thanks for posting and welcome to the community. It is always interesting to see what applications people are interested in. I would refer you to the KB on the BFAST source. This source is fundamentally different than other sources in FDTD, so special care is required. In particular it is more numerically unstable than the FDTD solver, as discussed in the link I posted. It seems you have had success with it but divergence becomes an issue at stepper injection angles. The believe the issue is related to the PML, since I was able to get your simulation to converge at 75 degrees by using steep angle PML.
One other thing that you should consider is the bandwidth of your simulation. Typically we recommend an order of magnitude or less, and so the 200-4000nm is likely too broad. I looked at the material explorer and the multi coefficient fit for Tungsten was not very accurate.
To properly model some of the important interactions the paper mentions, such plasmon-polariton or band-gap resonance, you should try and improve the fit. Reducing fit tolerance, and increasing number of coefficients will help. Also this would be easier if you split the bandwidth in two simulations.