The Red Cedar might be the go to... I built a few out of that and had to add a little more arse weight to get them to sit where I wanted. Good tip on the extra weight... I found some 3/8 eggs with a 3/32 thru hole that helped out too.
I built some out of Poplar last spring, that sat just like you say, with the middle size tail weight from NJT, might be worth a shot
