SNAIL E Dorian is pretty common,Morrisons jig,Trip to kilavil,The arran boat[air]TheBoatman[air],Ill go and enlist for a sailor[Cotswold Morris Sherborne],Bog an lochan[strathspey] to name a few.,in my experience E aeolian is less common,but it does occur.
The important thing is that you dont have to use an e minor chord,You can use a dyad[two note chord]consisting of root and fifth doubled,I call it Emodal,and it is not difficult in standard tuning.,It can be SUBSTITUTED for Emajor, or an E MINOR CHORD.