I found this band that looks like it's just starting called Vernon Jane. They released an EP in 2015 and a single called "Fuck Me" this year. Sounds like garage-rock had a lovechild with jazz-rock. Singer's voice sounds a little castrating though. I dunno, what do you think /mu/?
Fuck Me - https://www.youtube.com/watch?v=Ojx3Fy_5pns
It's good. The singer voice was better than you described it.