Good luck with the audition! Getting along with everyone is pretty important for me. I was playing with some guys a few years ago that decided they wanted to switch gears and do a grunge tribute band. The singer 100% could nail Cornell stuff, we did some Soundgarden etc. It wasn’t for me, so I left. Then the bass player started another band and asked me to play amd with a singer I worked with before. We all get along great and fortunately are all good players too.
Stage presence with Grunge? Is that a thing? Seems a flannel shirt and some work boots to stare at is enough.

Seriously though, you should be able to get those tones with about anything really. Just dial up more low and low mid and get the fx right when needed. Get the parts down and go have some fun!