I play in a similar situation, singer songwriter, that has a similar feel to Amos Lee, and I record with him often. I also play with a jazz quartet, classic rock cover band, an indy rock band, and a rotating member jazz fusion thing with elements of latin. I believe strongly that each situation requires a different sound from the drummer. Although I find that it's more about the instruments you choose, the implement you use, tuning, and playing style than about the heads.
I mean don't get me wrong, some heads just don't work in certain situations.
So with the singer guy I use some hand drums incorporated with the kit. On one tune I added jingles on a 16" djembe and played it with plastic brushes, taped to be firm, in place of the snare.
I also believe that certain drums sound best (very subjective) with certain heads. So I buy drums/sets with the gig in mind and then use the heads and tuning which sounds best (subjective) for that situation.
All that said, I use a Rogers Powertone kit with the singer guy with Remo Fiberskyn 3 Ambassadors on top and bottom of the the rogers toms, tuned exactly the same with a small moon jell on the top. I use an Aquarian Super Kick II batter and black Evans Resonant on the bass drum. Sometimes I play the snare with the snares off and use wire brushes in place of sticks as well.
Don't know if that helps but just wanted to weigh in.