I only use amp plug ins when I am making demos for the band but I do find I have to EQ them. Sometimes I will also run them through a preamp plug in for more warmth.
I have been using Nut Sauce for years it works as advertised. Especially on my trem guitars. I also have graphite, but as you said, it is dirty and IMO it doesn't work as well.
I had the WLH set in my Custom Lite they sounded amazing. The only reason I took them out is I needed something closer to the tonal vibe my band has. I put a gold Black Winter set in it and the guitar blows you skirt up but still has the classic vibe. I would have no problem putting the WLHs...