Circumaural. Glad you asked. At least you don't spell bass as base.
I own the S4 and have tried the first two on your list. To me, the TMA-1 is dark compared to the S4 to the point of veiled. Much of the high end just isn't there. I think the M-80 has a superior sound to the S4, especially in the mid range- much smoother vocals. From what I have read, the LP2 is a bassmonster that is also dark. Momentum is one I would like to hear and I would suggest checking out that thread for more detail. From what you describe, you may like the M-80. V-Moda offers a 60 day return if you don't.
You can't beat a bit of base!
Cheers for the reply, how do you think the M80s bass compares to the S4 as for me, it is that outstanding feature that I am trying to find in a headphone.