You have to fish what you have confidence in. You might loose just a tad bit of sensitivity going to the slower action, but may not be noticeable. The rods you have listed will all work well, and I own a few of each. The LTB is my choice for sensitivity, with the Dobyns and Avid being very close I just think the LTB is a little crisper. In terms of balance the Dobyns wins that easily, the Avid and LTB both can seem just a bit heavy in the tip when you get into some of the longer rods.
For me when you talk contact baits, sensitivity is king, and for that reason alone, I would choose the LTB over the other two, but not by much. Between the Dobyns and the Avid, I choose the Dobyns, I think the sensitivity between the two is too close to call and may be model specific, but with the better balance going to the Dobyns that would be my order of preference.
LTB, Champion, Avid