You can emulate white musks with some of the following notes
helichrysum (also known as immortelle. The essential oil of this smells a bit like dry hay/lemon/white musk, especially as it dries down. The absolute of immortelle smells much different - more like maple syrup!)
opoponax
ambrette
If you want to add some dirtier musk elements, add a tiny bit of one or more of the following:
valerian root essential oil (funky with a coniferous topnote) or valerian root C02 extraction (funkier, with a funk smell throughout)
costus (have not used this as it's IFRA restricted but is supposed to smell musky/wet dog-ish)
cepes absolute (this is the absolute of a mushroom. Smells earthy, mushroomy, and kind of like dirt)
patchouli or spikenard